Diffusion of Random Walk in a Random Environment
| Author | : Lester N. Coyle |
| Publisher | : |
| Total Pages | : 298 |
| Release | : 1995 |
| Genre | : |
| ISBN | : |
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Random Walks and Random Environments: Random environments
| Author | : Barry D. Hughes |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 550 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 9780198537892 |
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This is the second volume of a two-volume work devoted to probability theory in physical chemistry, and engineering. Rather than dealing explicitly with the idea of an ongoing random walk, with each chaotic step taking place at fixed time intervals, this volume addresses random environments-- models in which the disorder is frozen in space. It begins with an introduction to the geometry of random environments, emphasizing Bernoulli percolation models. The scope of the investigation then widens as we ask how structural disorder affects the transport process. The final chapters confront the interplay of two different forms of randomness; spatial randomness frozen into the environment and temporal randomness associated with the choices for next steps made by a random walker. The book ends with a discussion of "the ant in the labyrinth" problems and an extensive bibliography that, along with the rest of the material, will be of value to researchers in physics, mathematics, and chemical engineering.
Two-Dimensional Random Walk
| Author | : Serguei Popov |
| Publisher | : Cambridge University Press |
| Total Pages | : 224 |
| Release | : 2021-03-18 |
| Genre | : Mathematics |
| ISBN | : 1108472451 |
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A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
Random Walk in Random and Non-random Environments
| Author | : P l Rvsz |
| Publisher | : World Scientific |
| Total Pages | : 421 |
| Release | : 2013 |
| Genre | : Mathematics |
| ISBN | : 981444751X |
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The simplest mathematical model of the Brownian motion of physics is the simple, symmetric random walk. This book collects and compares current results OCo 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 on Disordered Media and their Scaling Limits
| Author | : Takashi Kumagai |
| Publisher | : Springer |
| Total Pages | : 147 |
| Release | : 2014-01-25 |
| Genre | : Mathematics |
| ISBN | : 331903152X |
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In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory. Recently, there has been significant progress on the theory of random walk on disordered media such as fractals and random media. Random walk on a percolation cluster(‘the ant in the labyrinth’)is one of the typical examples. In 1986, H. Kesten showed the anomalous behavior of a random walk on a percolation cluster at critical probability. Partly motivated by this work, analysis and diffusion processes on fractals have been developed since the late eighties. As a result, various new methods have been produced to estimate heat kernels on disordered media. These developments are summarized in the notes.
Particles in the Coastal Ocean
| Author | : Daniel R. Lynch |
| Publisher | : Cambridge University Press |
| Total Pages | : 545 |
| Release | : 2015 |
| Genre | : Science |
| ISBN | : 110706175X |
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This book summarizes the modeling of the transport, evolution and fate of particles in the coastal ocean for advanced students and researchers.
Random Walks and Diffusion
| Author | : Open University Course Team |
| Publisher | : |
| Total Pages | : 200 |
| Release | : 2009-10-21 |
| Genre | : Diffusion |
| ISBN | : 9780749251680 |
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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.
Random Walk In Random And Non-random Environments (Second Edition)
| Author | : Revesz Pal |
| Publisher | : World Scientific |
| Total Pages | : 396 |
| Release | : 2005-08-11 |
| Genre | : Mathematics |
| ISBN | : 9814480223 |
Download Random Walk In Random And Non-random Environments (Second Edition) Book in PDF, ePub and Kindle
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 edition was published in 1990, a number of new results have appeared in the literature. The original edition contained many unsolved problems and conjectures which have since been settled; this second revised and enlarged edition includes those new results. Three new chapters have been added: frequently and rarely visited points, heavy points and long excursions. This new edition presents the most complete study of, and the most elementary way to study, the path properties of the Brownian motion.
Non-homogeneous Random Walks
| Author | : Mikhail Menshikov |
| Publisher | : Cambridge University Press |
| Total Pages | : 423 |
| Release | : 2016-12-22 |
| Genre | : Mathematics |
| ISBN | : 1316867366 |
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Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.
Random Walks in a Random Environment
| Author | : Frederick Charles Solomon |
| Publisher | : |
| Total Pages | : 162 |
| Release | : 1972 |
| Genre | : Random walks (Mathematics) |
| ISBN | : |
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