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Branching Random Walks
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Book Synopsis Branching Random Walks by : Zhan Shi
Download or read book Branching Random Walks written by Zhan Shi and published by Springer. This book was released on 2016-02-04 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Branching Random Walks in Nonhomogenous Environments by : Elena Yarovaya
Download or read book Branching Random Walks in Nonhomogenous Environments written by Elena Yarovaya and published by John Wiley & Sons. This book was released on 2023-06-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to a modern section of the probability theory, the so-called theory of branching random walks. Chapter 1 describes the random walk model in the finite branching one-source environment. Chapter 2 is devoted to a model of homogeneous, symmetrical, irreducible random walk (without branching) with finite variance of the jumps on the multidimensional integer continuous-time lattice where transition is possible to an arbitrary point of the lattice and not only to the neighbor state. This model is a generalization of the simple symmetrical random walk often encountered in the applied studies. In Chapter 3 the branching random walk is studied by means of the spectral methods. Here, the property of monotonicity of the mean number of particles in the source plays an important role in the subsequent parts of the book. Chapter 4 demonstrates that existence of an isolated positive eigenvalue in the spectrum of unperturbed random walk generator defines the exponential growth of the process in the supercritical case. Chapter 5 exemplify application of the Tauberian theorems in the asymptotical problems of the probability theory. At last, the final Chapters 6 and 7 are devoted to detailed examination of survival probabilities in the critical and subcritical cases.
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.
Book Synopsis Studies in One Dimensional Branching Random Walks by : Ming Fang
Download or read book Studies in One Dimensional Branching Random Walks written by Ming Fang and published by . This book was released on 2011 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Combinatorial Stochastic Processes by : Jim Pitman
Download or read book Combinatorial Stochastic Processes written by Jim Pitman and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.
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 Asymptotic Analysis of Random Walks by : A. A. Borovkov
Download or read book Asymptotic Analysis of Random Walks written by A. A. Borovkov and published by Cambridge University Press. This book was released on 2020-10-29 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.
Book Synopsis Probability on Trees and Networks by : Russell Lyons
Download or read book Probability on Trees and Networks written by Russell Lyons and published by Cambridge University Press. This book was released on 2017-01-20 with total page 1023 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.
Book Synopsis Variants of Random Walks by : Source Wikipedia
Download or read book Variants of Random Walks written by Source Wikipedia and published by Booksllc.Net. This book was released on 2013-09 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 24. Chapters: Branching random walk, Brownian motion, Gambler's ruin, Heterogeneous random walk in one dimension, Loop-erased random walk, Ornstein-Uhlenbeck process, Reflected Brownian motion, Wiener process. Excerpt: A random walk is a mathematical formalization of a path that consists of a succession of random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be modeled as random walks, although they may not be truly random in reality. The term random walk was first introduced by Karl Pearson in 1905. Random walks have been used in many fields: ecology, economics, psychology, computer science, physics, chemistry, and biology. Random walks explain the observed behaviors of processes in these fields, and thus serve as a fundamental model for the recorded stochastic activity. Various different types of random walks are of interest. Often, random walks are assumed to be Markov chains or Markov processes, but other, more complicated walks are also of interest. Some random walks are on graphs, others on the line, in the plane, or in higher dimensions, while some random walks are on groups. Random walks also vary with regard to the time parameter. Often, the walk is in discrete time, and indexed by the natural numbers, as in . However, some walks take their steps at random times, and in that case the position is defined for the continuum of times . Specific cases or limits of random walks include the Levy flight. Random walks are related to the diffusion models and are a fundamental topic in discussions of Markov processes. Several properties of random walks, including dispersal distributions, first-passage times and encounter rates, have been extensively studied. A popular random...
Book Synopsis Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis by : J. T. Cox
Download or read book Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis written by J. T. Cox and published by American Mathematical Soc.. This book was released on 2004 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the evolution of the large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. This title introduces the concept of a continuum limit in the hierarchical mean field limit.
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 Walks Of Infinitely Many Particles by : Pal Revesz
Download or read book Random Walks Of Infinitely Many Particles written by Pal Revesz and published by World Scientific. This book was released on 1994-09-12 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author's previous book, Random Walk in Random and Non-Random Environments, was devoted to the investigation of the Brownian motion of a simple particle. The present book studies the independent motions of infinitely many particles in the d-dimensional Euclidean space Rd. In Part I the particles at time t = 0 are distributed in Rd according to the law of a given random field and they execute independent random walks. Part II is devoted to branching random walks, i.e. to the case where the particles execute random motions and birth and death processes independently. Finally, in Part III, functional laws of iterated logarithms are proved for the cases of independent motions and branching processes.
Book Synopsis Branching Random Walks by : Soeren Asmussen
Download or read book Branching Random Walks written by Soeren Asmussen and published by . This book was released on 1975 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Walks of Infinitely Many Particles by : P l Rvsz
Download or read book Random Walks of Infinitely Many Particles written by P l Rvsz and published by World Scientific. This book was released on 1994 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author's previous book, Random Walk in Random and Non-Random Environments, was devoted to the investigation of the Brownian motion of a simple particle. The present book studies the independent motions of infinitely many particles in the d-dimensional Euclidean space Rd. In Part I the particles at time t = 0 are distributed in Rd according to the law of a given random field and they execute independent random walks. Part II is devoted to branching random walks, i.e. to the case where the particles execute random motions and birth and death processes independently. Finally, in Part III, functional laws of iterated logarithms are proved for the cases of independent motions and branching processes.
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 Limit Theorems for Branching Random Walks and Products of Random Matrices by : Thi Thuy Bui
Download or read book Limit Theorems for Branching Random Walks and Products of Random Matrices written by Thi Thuy Bui and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of my thesis is to establish limit theorems for a branching random walk with products of random matrices by taking advantage of recent advances in products of random matrices and establishing new results as needed.
Book Synopsis High Dimensional Annihilating Branching Random Walks by : Xiaolong Luo
Download or read book High Dimensional Annihilating Branching Random Walks written by Xiaolong Luo and published by . This book was released on 1990 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
