Principles Of Random Walk Zz
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Author | : Frank Spitzer |
Publisher | : Methuen Paperback |
Total Pages | : 0 |
Release | : 2022-12-22 |
Genre | : Mathematics |
ISBN | : 9781475742312 |
This book is devoted exclusively to a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space. The author considered this high degree of specialization worth while, because of the theory of such random walks is far more complete than that of any larger class of Markov chains. The book will present no technical difficulties to the readers with some solid experience in analysis in two or three of the following areas: probability theory, real variables and measure, analytic functions, Fourier analysis, differential and integral operators. There are almost 100 pages of examples and problems.
Author | : Frank Spitzer |
Publisher | : Springer Science & Business Media |
Total Pages | : 419 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475742290 |
This book is devoted exclusively to a very special class of random processes, namely, to random walk on the lattice points of ordinary Euclidian space. The author considers this high degree of specialization worthwhile because the theory of such random walks is far more complete than that of any larger class of Markov chains. Almost 100 pages of examples and problems are included.
Author | : Frank Ludvig Spitzer |
Publisher | : |
Total Pages | : 408 |
Release | : 1976 |
Genre | : Random walks (Mathematics) |
ISBN | : 9787506200646 |
Author | : Abram Skogseid |
Publisher | : |
Total Pages | : 0 |
Release | : 2011-10 |
Genre | : Engineering mathematics |
ISBN | : 9781614709664 |
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.
Author | : Serguei Popov |
Publisher | : Cambridge University Press |
Total Pages | : 224 |
Release | : 2021-03-18 |
Genre | : Mathematics |
ISBN | : 1108472451 |
A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.
Author | : Kôhei Uchiyama |
Publisher | : Springer Nature |
Total Pages | : 277 |
Release | : 2023 |
Genre | : Electronic books |
ISBN | : 3031410203 |
This book studies the potential functions of one-dimensional recurrent random walks on the lattice of integers with step distribution of infinite variance. The central focus is on obtaining reasonably nice estimates of the potential function. These estimates are then applied to various situations, yielding precise asymptotic results on, among other things, hitting probabilities of finite sets, overshoot distributions, Green functions on long finite intervals and the half-line, and absorption probabilities of two-sided exit problems. The potential function of a random walk is a central object in fluctuation theory. If the variance of the step distribution is finite, the potential function has a simple asymptotic form, which enables the theory of recurrent random walks to be described in a unified way with rather explicit formulae. On the other hand, if the variance is infinite, the potential function behaves in a wide range of ways depending on the step distribution, which the asymptotic behaviour of many functionals of the random walk closely reflects. In the case when the step distribution is attracted to a strictly stable law, aspects of the random walk have been intensively studied and remarkable results have been established by many authors. However, these results generally do not involve the potential function, and important questions still need to be answered. In the case where the random walk is relatively stable, or if one tail of the step distribution is negligible in comparison to the other on average, there has been much less work. Some of these unsettled problems have scarcely been addressed in the last half-century. As revealed in this treatise, the potential function often turns out to play a significant role in their resolution. Aimed at advanced graduate students specialising in probability theory, this book will also be of interest to researchers and engineers working with random walks and stochastic systems.
Author | : Frank Ludwig Spitzer |
Publisher | : |
Total Pages | : 0 |
Release | : 1964 |
Genre | : Random walks (Mathematics) |
ISBN | : |
Author | : H. Kesten |
Publisher | : Springer Science & Business Media |
Total Pages | : 457 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461204593 |
This collection of articles is dedicated to Frank Spitzer on the occasion of his 65th birthday. The articles, written by a group of his friends, colleagues, former students and coauthors, are intended to demonstrate the major influence Frank has had on probability theory for the last 30 years and most likely will have for many years to come. Frank has always liked new phenomena, clean formulations and elegant proofs. He has created or opened up several research areas and it is not surprising that many people are still working out the consequences of his inventions. By way of introduction we have reprinted some of Frank's seminal articles so that the reader can easily see for himself the point of origin for much of the research presented here. These articles of Frank's deal with properties of Brownian motion, fluctuation theory and potential theory for random walks, and, of course, interacting particle systems. The last area was started by Frank as part of the general resurgence of treating problems of statistical mechanics with rigorous probabilistic tools.
Author | : David W. Spitzer |
Publisher | : |
Total Pages | : 406 |
Release | : 1964 |
Genre | : Random walks (Mathematics) |
ISBN | : |
Author | : David A. Levin |
Publisher | : American Mathematical Soc. |
Total Pages | : 465 |
Release | : 2017-10-31 |
Genre | : Mathematics |
ISBN | : 1470429624 |
This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines. The central tools for estimating convergence times, including coupling, strong stationary times, and spectral methods, are developed. The authors discuss many examples, including card shuffling and the Ising model, from statistical mechanics, and present the connection of random walks to electrical networks and apply it to estimate hitting and cover times. The first edition has been used in courses in mathematics and computer science departments of numerous universities. The second edition features three new chapters (on monotone chains, the exclusion process, and stationary times) and also includes smaller additions and corrections throughout. Updated notes at the end of each chapter inform the reader of recent research developments.