Elements of Random Walk and Diffusion Processes

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1118617932
Total Pages : 280 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Elements of Random Walk and Diffusion Processes by : Oliver C. Ibe

Download or read book Elements of Random Walk and Diffusion Processes written by Oliver C. Ibe and published by John Wiley & Sons. This book was released on 2013-08-29 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic processes, the book presents the connections between diffusion equations and random motion. Standard methods and applications of Brownian motion are addressed in addition to Levy motion, which has become popular in random searches in a variety of fields. The book also covers fractional calculus and introduces percolation theory and its relationship to diffusion processes. With a strong emphasis on the relationship between random walk theory and diffusion processes, Elements of Random Walk and Diffusion Processes features: Basic concepts in probability, an overview of stochastic and fractional processes, and elements of graph theory Numerous practical applications of random walk across various disciplines, including how to model stock prices and gambling, describe the statistical properties of genetic drift, and simplify the random movement of molecules in liquids and gases Examples of the real-world applicability of random walk such as node movement and node failure in wireless networking, the size of the Web in computer science, and polymers in physics Plentiful examples and exercises throughout that illustrate the solution of many practical problems Elements of Random Walk and Diffusion Processes is an ideal reference for researchers and professionals involved in operations research, economics, engineering, mathematics, and physics. The book is also an excellent textbook for upper-undergraduate and graduate level courses in probability and stochastic processes, stochastic models, random motion and Brownian theory, random walk theory, and diffusion process techniques.

Random Walk and Diffusion Models

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Author :
Publisher : Springer Nature
ISBN 13 : 3031121007
Total Pages : 218 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Random Walk and Diffusion Models by : Wolf Schwarz

Download or read book Random Walk and Diffusion Models written by Wolf Schwarz and published by Springer Nature. This book was released on 2022-10-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an accessible introduction to random walk and diffusion models at a level consistent with the typical background of students in the life sciences. In recent decades these models have become widely used in areas far beyond their traditional origins in physics, for example, in studies of animal behavior, ecology, sociology, sports science, population genetics, public health applications, and human decision making. Developing the main formal concepts, the book provides detailed and intuitive step-by-step explanations, and moves smoothly from simple to more complex models. Finally, in the last chapter, some successful and original applications of random walk and diffusion models in the life and behavioral sciences are illustrated in detail. The treatment of basic techniques and models is consolidated and extended throughout by a set of carefully chosen exercises.

Random Walk and Diffusion Models

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Author :
Publisher :
ISBN 13 : 9783031121012
Total Pages : 0 pages
Book Rating : 4.1/5 (21 download)

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Book Synopsis Random Walk and Diffusion Models by : Wolfgang Schwarz

Download or read book Random Walk and Diffusion Models written by Wolfgang Schwarz and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an accessible introduction to random walk and diffusion models at a level consistent with the typical background of students in the life sciences. In recent decades these models have become widely used in areas far beyond their traditional origins in physics, for example, in studies of animal behavior, ecology, sociology, sports science, population genetics, public health applications, and human decision making. Developing the main formal concepts, the book provides detailed and intuitive step-by-step explanations, and moves smoothly from simple to more complex models. Finally, in the last chapter, some successful and original applications of random walk and diffusion models in the life and behavioral sciences are illustrated in detail. The treatment of basic techniques and models is consolidated and extended throughout by a set of carefully chosen exercises.

Mathematics of Evolution and Phylogeny

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Author :
Publisher : OUP Oxford
ISBN 13 : 9780191513732
Total Pages : 444 pages
Book Rating : 4.5/5 (137 download)

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Book Synopsis Mathematics of Evolution and Phylogeny by : Olivier Gascuel

Download or read book Mathematics of Evolution and Phylogeny written by Olivier Gascuel and published by OUP Oxford. This book was released on 2005-02-24 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers evolution at different scales: sequences, genes, gene families, organelles, genomes and species. The focus is on the mathematical and computational tools and concepts, which form an essential basis of evolutionary studies, indicate their limitations, and give them orientation. Recent years have witnessed rapid progress in the mathematics of evolution and phylogeny, with models and methods becoming more realistic, powerful, and complex. Aimed at graduates and researchers in phylogenetics, mathematicians, computer scientists and biologists, and including chapters by leading scientists: A. Bergeron, D. Bertrand, D. Bryant, R. Desper, O. Elemento, N. El-Mabrouk, N. Galtier, O. Gascuel, M. Hendy, S. Holmes, K. Huber, A. Meade, J. Mixtacki, B. Moret, E. Mossel, V. Moulton, M. Pagel, M.-A. Poursat, D. Sankoff, M. Steel, J. Stoye, J. Tang, L.-S. Wang, T. Warnow, Z. Yang, this book of contributed chapters explains the basis and covers the recent results in this highly topical area.

Elements of Random Walk and Diffusion Processes

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1118618092
Total Pages : 280 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Elements of Random Walk and Diffusion Processes by : Oliver C. Ibe

Download or read book Elements of Random Walk and Diffusion Processes written by Oliver C. Ibe and published by John Wiley & Sons. This book was released on 2013-09-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic processes, the book presents the connections between diffusion equations and random motion. Standard methods and applications of Brownian motion are addressed in addition to Levy motion, which has become popular in random searches in a variety of fields. The book also covers fractional calculus and introduces percolation theory and its relationship to diffusion processes. With a strong emphasis on the relationship between random walk theory and diffusion processes, Elements of Random Walk and Diffusion Processes features: Basic concepts in probability, an overview of stochastic and fractional processes, and elements of graph theory Numerous practical applications of random walk across various disciplines, including how to model stock prices and gambling, describe the statistical properties of genetic drift, and simplify the random movement of molecules in liquids and gases Examples of the real-world applicability of random walk such as node movement and node failure in wireless networking, the size of the Web in computer science, and polymers in physics Plentiful examples and exercises throughout that illustrate the solution of many practical problems Elements of Random Walk and Diffusion Processes is an ideal reference for researchers and professionals involved in operations research, economics, engineering, mathematics, and physics. The book is also an excellent textbook for upper-undergraduate and graduate level courses in probability and stochastic processes, stochastic models, random motion and Brownian theory, random walk theory, and diffusion process techniques.

First Steps in Random Walks

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Author :
Publisher : Oxford University Press
ISBN 13 : 0199234868
Total Pages : 161 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis First Steps in Random Walks by : J. Klafter

Download or read book First Steps in Random Walks written by J. Klafter and published by Oxford University Press. This book was released on 2011-08-18 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random walks proved to be a useful model of many complex transport processes at the micro and macroscopical level in physics and chemistry, economics, biology and other disciplines. The book discusses the main variants of random walks and gives the most important mathematical tools for their theoretical description.

Random Walk and the Heat Equation

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821848291
Total Pages : 170 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Random Walk and the Heat Equation by : Gregory F. Lawler

Download or read book Random Walk and the Heat Equation written by Gregory F. Lawler and published by American Mathematical Soc.. This book was released on 2010-11-22 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.

Random Walks and Diffusions on Graphs and Databases

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 364219592X
Total Pages : 271 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Random Walks and Diffusions on Graphs and Databases by : Philipp Blanchard

Download or read book Random Walks and Diffusions on Graphs and Databases written by Philipp Blanchard and published by Springer Science & Business Media. This book was released on 2011-05-26 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks.

Random Walks and Diffusion

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Author :
Publisher :
ISBN 13 : 9780749251680
Total Pages : 200 pages
Book Rating : 4.2/5 (516 download)

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Book Synopsis Random Walks and Diffusion by : Open University Course Team

Download or read book Random Walks and Diffusion written by Open University Course Team and published by . This book was released on 2009-10-21 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This block explores the diffusion equation which is most commonly encountered in discussions of the flow of heat and of molecules moving in liquids, but diffusion equations arise from many different areas of applied mathematics. As well as considering the solutions of diffusion equations in detail, we also discuss the microscopic mechanism underlying the diffusion equation, namely that particles of matter or heat move erratically. This involves a discussion of elementary probability and statistics, which are used to develop a description of random walk processes and of the central limit theorem. These concepts are used to show that if particles follow random walk trajectories, their density obeys the diffusion equation.

Elements of the Random Walk

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Author :
Publisher : Cambridge University Press
ISBN 13 : 9781139450140
Total Pages : 350 pages
Book Rating : 4.4/5 (51 download)

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Book Synopsis Elements of the Random Walk by : Joseph Rudnick

Download or read book Elements of the Random Walk written by Joseph Rudnick and published by Cambridge University Press. This book was released on 2004-03-04 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random walks have proven to be a useful model in understanding processes across a wide spectrum of scientific disciplines. Elements of the Random Walk is an introduction to some of the most powerful and general techniques used in the application of these ideas. The mathematical construct that runs through the analysis of the topics covered in this book, unifying the mathematical treatment, is the generating function. Although the reader is introduced to analytical tools, such as path-integrals and field-theoretical formalism, the book is self-contained in that basic concepts are developed and relevant fundamental findings fully discussed. Mathematical background is provided in supplements at the end of each chapter, when appropriate. This text will appeal to graduate students across science, engineering and mathematics who need to understand the applications of random walk techniques, as well as to established researchers.

Particles in the Coastal Ocean

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Publisher : Cambridge University Press
ISBN 13 : 110706175X
Total Pages : 545 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Particles in the Coastal Ocean by : Daniel R. Lynch

Download or read book Particles in the Coastal Ocean written by Daniel R. Lynch and published by Cambridge University Press. This book was released on 2015 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the modeling of the transport, evolution and fate of particles in the coastal ocean for advanced students and researchers.

Two-Dimensional Random Walk

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Publisher : Cambridge University Press
ISBN 13 : 1108472451
Total Pages : 224 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Two-Dimensional Random Walk by : Serguei Popov

Download or read book Two-Dimensional Random Walk written by Serguei Popov and published by Cambridge University Press. This book was released on 2021-03-18 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.

Statistical Mechanics and Random Walks

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Publisher :
ISBN 13 : 9781614709664
Total Pages : 0 pages
Book Rating : 4.7/5 (96 download)

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Book Synopsis Statistical Mechanics and Random Walks by : Abram Skogseid

Download or read book Statistical Mechanics and Random Walks written by Abram Skogseid and published by . This book was released on 2011-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors gather and present topical research in the study of statistical mechanics and random walk principles and applications. Topics discussed in this compilation include the application of stochastic approaches to modelling suspension flow in porous media; subordinated Gaussian processes; random walk models in biophysical science; non-equilibrium dynamics and diffusion processes; global random walk algorithm for diffusion processes and application of random walks for the analysis of graphs, musical composition and language phylogeny.

Transformations of Materials

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Publisher : Morgan & Claypool Publishers
ISBN 13 : 1643276204
Total Pages : 184 pages
Book Rating : 4.6/5 (432 download)

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Book Synopsis Transformations of Materials by : Dimitri D Vvedensky

Download or read book Transformations of Materials written by Dimitri D Vvedensky and published by Morgan & Claypool Publishers. This book was released on 2019-09-30 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase transformations are among the most intriguing and technologically useful phenomena in materials, particularly with regard to controlling microstructure. After a review of thermodynamics, this book has chapters on Brownian motion and the diffusion equation, diffusion in solids based on transition-state theory, spinodal decomposition, nucleation and growth, instabilities in solidification, and diffusionless transformations. Each chapter includes exercises whose solutions are available in a separate manual. This book is based on the notes from a graduate course taught in the Centre for Doctoral Training in the Theory and Simulation of Materials. The course was attended by students with undergraduate degrees in physics, mathematics, chemistry, materials science, and engineering. The notes from this course, and this book, were written to accommodate these diverse backgrounds.

Random Walks in Biology

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Publisher : Princeton University Press
ISBN 13 : 1400820022
Total Pages : 166 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Random Walks in Biology by : Howard C. Berg

Download or read book Random Walks in Biology written by Howard C. Berg and published by Princeton University Press. This book was released on 2018-11-20 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles.

Percolation Theory and Ergodic Theory of Infinite Particle Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 1461387345
Total Pages : 322 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Percolation Theory and Ergodic Theory of Infinite Particle Systems by : Harry Kesten

Download or read book Percolation Theory and Ergodic Theory of Infinite Particle Systems written by Harry Kesten and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in ~athematics and its Applications PERCOLATION THEORY AND ERGODIC THEORY OF INFINITE PARTICLE SYSTEMS represents the proceedings of a workshop which was an integral part of the 19R4-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: naniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaoo for planning and implementing an exciting and stimulating year-long program. We especially thank the Workshop Organizing Committee, Harry Kesten (Chairman), Richard Holley, and Thomas Liggett for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinherger PREFACE Percolation theory and interacting particle systems both have seen an explosive growth in the last decade. These suhfields of probability theory are closely related to statistical mechanics and many of the publications on these suhjects (especially on the former) appear in physics journals, wit~ a great variahility in the level of rigour. There is a certain similarity and overlap hetween the methods used in these two areas and, not surprisingly, they tend to attract the same probabilists. It seemed a good idea to organize a workshop on "Percolation Theory and Ergodic Theory of Infinite Particle Systems" in the framework of the special probahility year at the Institute for Mathematics and its Applications in 1985-86. Such a workshop, dealing largely with rigorous results, was indeed held in February 1986.

Random Walk Models Arising in Double Diffusion and Related Applications

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Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.:/5 (215 download)

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Book Synopsis Random Walk Models Arising in Double Diffusion and Related Applications by : Liwan H. Liyanage

Download or read book Random Walk Models Arising in Double Diffusion and Related Applications written by Liwan H. Liyanage and published by . This book was released on 1983 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: