Random Walks And Random Environments

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Random Walks And Random Environments

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Author : Barry D. Hughes
language : en
Publisher:
Release Date : 1995

Random Walks And Random Environments written by Barry D. Hughes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Chemistry, Physical and theoretical categories.

Random Walk In Random And Non Random Environments Third Edition

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Author : Pal Revesz
language : en
Publisher: World Scientific
Release Date : 2013-03-06

Random Walk In Random And Non Random Environments Third Edition written by Pal Revesz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-06 with Mathematics categories.

The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results — mostly strong theorems which describe the properties of a random walk. The modern problems of the limit theorems of probability theory are treated in the simple case of coin tossing. Taking advantage of this simplicity, the reader is familiarized with limit theorems (especially strong ones) without the burden of technical tools and difficulties. An easy way of considering the Wiener process is also given, through the study of the random walk.Since the first and second editions were published in 1990 and 2005, a number of new results have appeared in the literature. The first two editions contained many unsolved problems and conjectures which have since been settled; this third, revised and enlarged edition includes those new results. In this edition, a completely new part is included concerning Simple Random Walks on Graphs. Properties of random walks on several concrete graphs have been studied in the last decade. Some of the obtained results are also presented.

Random Walks And Random Environments

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Author : Barry D. Hughes
language : en
Publisher:
Release Date : 2023

Random Walks And Random Environments written by Barry D. Hughes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Mathematical physics categories.

Random Walks And Random Environments

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Author : B. D. Hughes
language : en
Publisher:
Release Date : 2023

Random Walks And Random Environments written by B. D. Hughes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Chemistry, Physical and theoretical categories.

This volume is devoted to probability theory in physics, physical chemistry and engineering. It provides an introduction to the problem of "random walk" and its applications. A prior knowledge of probability theory is helpful, but not assumed.

Asymptotic Analysis Of Random Walks

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Author : Aleksandr Alekseevich Borovkov
language : en
Publisher: Cambridge University Press
Release Date : 2008

Asymptotic Analysis Of Random Walks written by Aleksandr Alekseevich Borovkov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Asymptotic expansions categories.

This monograph is devoted to studying the asymptotic behaviour of the probabilities of large deviations of the trajectories of random walks, with 'heavy-tailed' (in particular, regularly varying, sub- and semiexponential) jump distributions. It presents a unified and systematic exposition.

An Unbounded Experience In Random Walks With Applications

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Author : Michael F Shlesinger
language : en
Publisher: World Scientific
Release Date : 2021-06-29

An Unbounded Experience In Random Walks With Applications written by Michael F Shlesinger and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-29 with Mathematics categories.

This volume comprises the author's account of the development of novel results in random walk theory and its applications during the fractal and chaos revolutions. The early history of probability is presented in an engaging manner, and peppered with pitfalls and paradoxes. Readers will find the introduction of Paul Lévy's work via Mandelbrot's Lévy flights which are featured uniquely as Weierstrass and Riemann random walks.Generalizations to coupled memories, internal states and fractal time are introduced at the level for graduate students. Mathematical developments are explained including Green's functions, inverse Mellin transforms, Jacobians, and matrix methods. Applications are made to anomalous diffusion and conductivity in amorphous semiconductors and supercooled liquids. The glass transition is discussed especially for pressure effects.All along the way, personal stories are recounted and special appreciations are made to Elliott Montroll and Harvey Scher for their ever-expanding influence on the field of non-equilibrium anomalous processes that now are found in topics including disordered materials, water table processes, animal foraging, blinking quantum dots, rotating flows, optical lattices, dynamical strange attractors and strange kinetics.

Random Walk A Modern Introduction

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Author : Gregory F. Lawler
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24

Random Walk A Modern Introduction written by Gregory F. Lawler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.

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.

The Parabolic Anderson Model

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Author : Wolfgang König
language : en
Publisher: Birkhäuser
Release Date : 2016-06-30

The Parabolic Anderson Model written by Wolfgang König and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-30 with Mathematics categories.

This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.

Branching Random Walks

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Author : Zhan Shi
language : en
Publisher: Springer
Release Date : 2016-02-04

Branching Random Walks written by Zhan Shi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-04 with Mathematics categories.

Providing an elementary introduction to branching random walks, the main focus of these lecture notes is on the asymptotic properties of one-dimensional discrete-time supercritical branching random walks, and in particular, on extreme positions in each generation, as well as the evolution of these positions over time. Starting with the simple case of Galton-Watson trees, the text primarily concentrates on exploiting, in various contexts, the spinal structure of branching random walks. The notes end with some applications to biased random walks on trees.