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Random Walks And Geometry
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Book Synopsis Random Walks and Geometry by : Vadim Kaimanovich
Download or read book Random Walks and Geometry written by Vadim Kaimanovich and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die jüngsten Entwicklungen zeigen, dass sich Wahrscheinlichkeitsverfahren zu einem sehr wirkungsvollen Werkzeug entwickelt haben, und das auf so unterschiedlichen Gebieten wie statistische Physik, dynamische Systeme, Riemann'sche Geometrie, Gruppentheorie, harmonische Analyse, Graphentheorie und Informatik.
Book Synopsis Combinatorial and Computational Geometry by : Jacob E. Goodman
Download or read book Combinatorial and Computational Geometry written by Jacob E. Goodman and published by Cambridge University Press. This book was released on 2005-08-08 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.
Book Synopsis Random Walks on Infinite Graphs and Groups by : Wolfgang Woess
Download or read book Random Walks on Infinite Graphs and Groups written by Wolfgang Woess and published by Cambridge University Press. This book was released on 2000-02-13 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
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.
Book Synopsis The Random Walks of George Polya by : Gerald L. Alexanderson
Download or read book The Random Walks of George Polya written by Gerald L. Alexanderson and published by Cambridge University Press. This book was released on 2000-04-27 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both a biography of Plya's life, and a review of his many mathematical achievements by today's experts.
Book Synopsis Topics in Groups and Geometry by : Tullio Ceccherini-Silberstein
Download or read book Topics in Groups and Geometry written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2022-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
Book Synopsis Random Walks and Electric Networks by : Peter G. Doyle
Download or read book Random Walks and Electric Networks written by Peter G. Doyle and published by American Mathematical Soc.. This book was released on 1984-12-31 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability theory, like much of mathematics, is indebted to physics as a source of problems and intuition for solving these problems. Unfortunately, the level of abstraction of current mathematics often makes it difficult for anyone but an expert to appreciate this fact. Random Walks and electric networks looks at the interplay of physics and mathematics in terms of an example—the relation between elementary electric network theory and random walks —where the mathematics involved is at the college level.
Book Synopsis Random Walks on Infinite Groups by : Steven P. Lalley
Download or read book Random Walks on Infinite Groups written by Steven P. Lalley and published by Springer Nature. This book was released on 2023-05-08 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.
Book Synopsis Planar Maps, Random Walks and Circle Packing by : Asaf Nachmias
Download or read book Planar Maps, Random Walks and Circle Packing written by Asaf Nachmias and published by Springer Nature. This book was released on 2019-10-04 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.
Book Synopsis Random Walks and Geometry by : Vadim A. Kaimanovich
Download or read book Random Walks and Geometry written by Vadim A. Kaimanovich and published by . This book was released on 2004 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments show that probability methods have become a very powerful tool in such different areas as statistical physics, dynamical systems, Riemannian geometry, group theory, harmonic analysis, graph theory and computer science. This volume is an outcome of the special semester 2001 - Random Walks held at the Schrodinger Institute in Vienna, Austria. It contains original research articles with non-trivial new approaches based on applications of random walks and similar processes to Lie groups, geometric flows, physical models on infinite graphs, random number generators, Lyapunov exponents, geometric group theory, spectral theory of graphs and potential theory. Highlights are the first survey of the theory of the stochastic Loewner evolution and its applications to percolation theory (a new rapidly developing and very promising subject at the crossroads of probability, statistical physics and harmonic analysis), surveys on expander graphs, random matrices and quantum chaos, cellular automata and symbolic dynamical systems, and others. The contributors to the volume are the leading experts in the area."
Book Synopsis A Random Walk Through Fractal Dimensions by : Brian H. Kaye
Download or read book A Random Walk Through Fractal Dimensions written by Brian H. Kaye and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science. From reviews of the first edition: "...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems." MRS Bulletin
Author :Tullio Ceccherini-Silberstein Publisher :Cambridge University Press ISBN 13 :1316817784 Total Pages :539 pages Book Rating :4.3/5 (168 download)
Book Synopsis Groups, Graphs and Random Walks by : Tullio Ceccherini-Silberstein
Download or read book Groups, Graphs and Random Walks written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2017-06-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubtedly stem.
Book Synopsis Random Walks and Heat Kernels on Graphs by : M. T. Barlow
Download or read book Random Walks and Heat Kernels on Graphs written by M. T. Barlow and published by Cambridge University Press. This book was released on 2017-02-23 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful but hard-to-find results enrich this introduction to the analytic study of random walks on infinite graphs.
Book Synopsis Random Walks on Reductive Groups by : Yves Benoist
Download or read book Random Walks on Reductive Groups written by Yves Benoist and published by Springer. This book was released on 2016-10-20 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical theory of random walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Book Synopsis Random Walk, Brownian Motion, and Martingales by : Rabi Bhattacharya
Download or read book Random Walk, Brownian Motion, and Martingales written by Rabi Bhattacharya and published by Springer Nature. This book was released on 2021-09-20 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. Consisting of many short chapters, the book begins with a comprehensive account of the simple random walk in one dimension. From here, different paths may be chosen according to interest. Themes span Poisson processes, branching processes, the Kolmogorov–Chentsov theorem, martingales, renewal theory, and Brownian motion. Special topics follow, showcasing a selection of important contemporary applications, including mathematical finance, optimal stopping, ruin theory, branching random walk, and equations of fluids. Engaging exercises accompany the theory throughout. Random Walk, Brownian Motion, and Martingales is an ideal introduction to the rigorous study of stochastic processes. Students and instructors alike will appreciate the accessible, example-driven approach. A single, graduate-level course in probability is assumed.
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.
