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A Condition For Weak Disorder For Directed Polymers In Random Environment
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Book Synopsis Directed Polymers in Random Environments by : Francis Comets
Download or read book Directed Polymers in Random Environments written by Francis Comets and published by Springer. This book was released on 2017-01-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
Author : Publisher :World Scientific ISBN 13 : Total Pages :1131 pages Book Rating :4./5 ( download)
Download or read book written by and published by World Scientific. This book was released on with total page 1131 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Polymers by : Frank Hollander
Download or read book Random Polymers written by Frank Hollander and published by Springer Science & Business Media. This book was released on 2009-05-14 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymer chains that interact with themselves and/or their environment display a range of physical and chemical phenomena. This text focuses on the mathematical description of some of these phenomena, offering a mathematical panorama of polymer chains.
Author :Clay Mathematics Institute. Summer School Publisher :American Mathematical Soc. ISBN 13 :0821868632 Total Pages :481 pages Book Rating :4.8/5 (218 download)
Book Synopsis Probability and Statistical Physics in Two and More Dimensions by : Clay Mathematics Institute. Summer School
Download or read book Probability and Statistical Physics in Two and More Dimensions written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2012 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of lecture notes for six of the ten courses given in Buzios, Brazil by prominent probabilists at the 2010 Clay Mathematics Institute Summer School, ``Probability and Statistical Physics in Two and More Dimensions'' and at the XIV Brazilian School of Probability. In the past ten to fifteen years, various areas of probability theory related to statistical physics, disordered systems and combinatorics have undergone intensive development. A number of these developments deal with two-dimensional random structures at their critical points, and provide new tools and ways of coping with at least some of the limitations of Conformal Field Theory that had been so successfully developed in the theoretical physics community to understand phase transitions of two-dimensional systems. Included in this selection are detailed accounts of all three foundational courses presented at the Clay school--Schramm-Loewner Evolution and other Conformally Invariant Objects, Noise Sensitivity and Percolation, Scaling Limits of Random Trees and Planar Maps--together with contributions on Fractal and Multifractal properties of SLE and Conformal Invariance of Lattice Models. Finally, the volume concludes with extended articles based on the courses on Random Polymers and Self-Avoiding Walks given at the Brazilian School of Probability during the final week of the school. Together, these notes provide a panoramic, state-of-the-art view of probability theory areas related to statistical physics, disordered systems and combinatorics. Like the lectures themselves, they are oriented towards advanced students and postdocs, but experts should also find much of interest.
Book Synopsis Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by : Rajendra Bhatia
Download or read book Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures written by Rajendra Bhatia and published by World Scientific. This book was released on 2011-06-06 with total page 4137 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
Book Synopsis Markov Processes and Related Fields by :
Download or read book Markov Processes and Related Fields written by and published by . This book was released on 2007 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Polymer Models by : Giambattista Giacomin
Download or read book Random Polymer Models written by Giambattista Giacomin and published by Imperial College Press. This book was released on 2007 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces readers to the world of disordered systems and to some of the remarkable probabilistic techniques developed in the field. The author explores in depth a class of directed polymer models to which much attention has been devoted in the last 25 years, in particular in the fields of physical and biological sciences. The models treated have been widely used in studying, for example, the phenomena of polymer pinning on a defect line, the behavior of copolymers in proximity to an interface between selective solvents and the DNA denaturation transition. In spite of the apparent heterogeneity of this list, in mathematical terms, a unified vision emerges. One is in fact dealing with the natural statistical mechanics systems built on classical renewal sequences by introducing one-body potentials. This volume is also a self-contained mathematical account of the state of the art for this class of statistical mechanics models.
Book Synopsis Lectures on Random Lozenge Tilings by : Vadim Gorin
Download or read book Lectures on Random Lozenge Tilings written by Vadim Gorin and published by Cambridge University Press. This book was released on 2021-09-09 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.
Book Synopsis Branching Processes by : Krishna B. Athreya
Download or read book Branching Processes written by Krishna B. Athreya and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro cess, etc. We have tried to avoid the rather uneconomical and un enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.
Book Synopsis Simulation Methods for Polymers by : Michael Kotelyanskii
Download or read book Simulation Methods for Polymers written by Michael Kotelyanskii and published by CRC Press. This book was released on 2004-03-01 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analytic Combinatorics by : Philippe Flajolet
Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Book Synopsis Random Growth Models by : Michael Damron
Download or read book Random Growth Models written by Michael Damron and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.
Book Synopsis Intersections of Random Walks by : Gregory F. Lawler
Download or read book Intersections of Random Walks written by Gregory F. Lawler and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which has applications in many areas, particularly in statistical physics and statistical chemistry. Originally published in 1991, Intersections of Random Walks focuses on and explores a number of problems dealing primarily with the nonintersection of random walks and the self-avoiding walk. Many of these problems arise in studying statistical physics and other critical phenomena. Topics include: discrete harmonic measure, including an introduction to diffusion limited aggregation (DLA); the probability that independent random walks do not intersect; and properties of walks without self-intersections. The present softcover reprint includes corrections and addenda from the 1996 printing, and makes this classic monograph available to a wider audience. With a self-contained introduction to the properties of simple random walks, and an emphasis on rigorous results, the book will be useful to researchers in probability and statistical physics and to graduate students interested in basic properties of random walks.
Download or read book Polymer Solutions written by Iwao Teraoka and published by John Wiley & Sons. This book was released on 2004-04-07 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polymer Solutions: An Introduction to Physical Properties offers a fresh, inclusive approach to teaching the fundamentals of physical polymer science. Students, instructors, and professionals in polymer chemistry, analytical chemistry, organic chemistry, engineering, materials, and textiles will find Iwao Teraoka’s text at once accessible and highly detailed in its treatment of the properties of polymers in the solution phase. Teraoka’s purpose in writing Polymer Solutions is twofold: to familiarize the advanced undergraduate and beginning graduate student with basic concepts, theories, models, and experimental techniques for polymer solutions; and to provide a reference for researchers working in the area of polymer solutions as well as those in charge of chromatographic characterization of polymers. The author’s incorporation of recent advances in the instrumentation of size-exclusion chromatography, the method by which polymers are analyzed, renders the text particularly topical. Subjects discussed include: Real, ideal, Gaussian, semirigid, and branched polymer chains Polymer solutions and thermodynamics Static light scattering of a polymer solution Dynamic light scattering and diffusion of polymers Dynamics of dilute and semidilute polymer solutions Study questions at the end of each chapter not only provide students with the opportunity to test their understanding, but also introduce topics relevant to polymer solutions not included in the main text. With over 250 geometrical model diagrams, Polymer Solutions is a necessary reference for students and for scientists pursuing a broader understanding of polymers.
Book Synopsis Random Walk: A Modern Introduction by : Gregory F. Lawler
Download or read book Random Walk: A Modern Introduction written by Gregory F. Lawler and published by Cambridge University Press. This book was released on 2010-06-24 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.
Book Synopsis Condensed Matter Field Theory by : Alexander Altland
Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
