Random Walks Brownian Motion And Interacting Particle Systems
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Random Walks Brownian Motion And Interacting Particle Systems
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Author : H. Kesten
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random Walks Brownian Motion And Interacting Particle Systems written by H. Kesten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Random Walks Brownian Motion And Interacting Particle Systems
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Author : H. Kesten
language : en
Publisher:
Release Date : 1991-06-01
Random Walks Brownian Motion And Interacting Particle Systems written by H. Kesten and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-01 with categories.
Lectures On Probability Theory
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Author : Philippe Biane
language : en
Publisher: Springer
Release Date : 2006-11-14
Lectures On Probability Theory written by Philippe Biane and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This book contains two of the three lectures given at the Saint-Flour Summer School of Probability Theory during the period August 18 to September 4, 1993.
Phase Transitions Of Interacting Particle Systems
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Author : Norio Konno
language : en
Publisher: World Scientific
Release Date : 1995-01-16
Phase Transitions Of Interacting Particle Systems written by Norio Konno and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-16 with Mathematics categories.
Recently, interacting particle systems have been studied widely from the standpoints of mathematics, physics, chemistry and biology. Many researchers are becoming interested in this field.This book focuses on the phase transitions of interacting particle systems, especially their critical values and order parameters. It poses the following question: How can we get good bounds on the critical values and the order parameters? This question is very basic, and many researchers have been trying to get better bounds rigorously. Hence the book provides bounds — both the author's and others'.
Probability And Phase Transition
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Author : G.R. Grimmett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Probability And Phase Transition written by G.R. Grimmett and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
This volume describes the current state of knowledge of random spatial processes, particularly those arising in physics. The emphasis is on survey articles which describe areas of current interest to probabilists and physicists working on the probability theory of phase transition. Special attention is given to topics deserving further research. The principal contributions by leading researchers concern the mathematical theory of random walk, interacting particle systems, percolation, Ising and Potts models, spin glasses, cellular automata, quantum spin systems, and metastability. The level of presentation and review is particularly suitable for postgraduate and postdoctoral workers in mathematics and physics, and for advanced specialists in the probability theory of spatial disorder and phase transition.
Continuous Martingales And Brownian Motion
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Author : Daniel Revuz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Continuous Martingales And Brownian Motion written by Daniel Revuz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
From the reviews: "This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..." Bull.L.M.S. 24, 4 (1992) Since the first edition in 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions.
The Theory Of Gambling And Statistical Logic
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Author : Richard A. Epstein
language : en
Publisher: Academic Press
Release Date : 2009-09-28
The Theory Of Gambling And Statistical Logic written by Richard A. Epstein and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-28 with Games & Activities categories.
Early in his rise to enlightenment, man invented a concept that has since been variously viewed as a vice, a crime, a business, a pleasure, a type of magic, a disease, a folly, a weakness, a form of sexual substitution, an expression of the human instinct. He invented gambling. Recent advances in the field, particularly Parrondo's paradox, have triggered a surge of interest in the statistical and mathematical theory behind gambling. This interest was acknowledge in the motion picture, "21," inspired by the true story of the MIT students who mastered the art of card counting to reap millions from the Vegas casinos. Richard Epstein's classic book on gambling and its mathematical analysis covers the full range of games from penny matching to blackjack, from Tic-Tac-Toe to the stock market (including Edward Thorp's warrant-hedging analysis). He even considers whether statistical inference can shed light on the study of paranormal phenomena. Epstein is witty and insightful, a pleasure to dip into and read and rewarding to study. The book is written at a fairly sophisticated mathematical level; this is not "Gambling for Dummies" or "How To Beat The Odds Without Really Trying." A background in upper-level undergraduate mathematics is helpful for understanding this work. - Comprehensive and exciting analysis of all major casino games and variants - Covers a wide range of interesting topics not covered in other books on the subject - Depth and breadth of its material is unique compared to other books of this nature - Richard Epstein's website: www.gamblingtheory.net
Random Walk Brownian Motion And Martingales
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Author : Rabi Bhattacharya
language : en
Publisher: Springer Nature
Release Date : 2021-09-20
Random Walk Brownian Motion And Martingales written by Rabi Bhattacharya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-20 with Mathematics categories.
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.
Probability Models For Dna Sequence Evolution
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Author : Rick Durrett
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Probability Models For Dna Sequence Evolution written by Rick Durrett and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Our basic question is: Given a collection of DNA sequences, what underlying forces are responsible for the observed patterns of variability? To approach this question we introduce and analyze a number of probability models: the Wright-Fisher model, the coalescent, the infinite alleles model, and the infinite sites model. We study the complications that come from nonconstant population size, recombination, population subdivision, and three forms of natural selection: directional selection, balancing selection, and background selection. These theoretical results set the stage for the investigation of various statistical tests to detect departures from "neutral evolution." The final chapter studies the evolution of whole genomes by chromosomal inversions, reciprocal translocations, and genome duplication. Throughout the book, the theory is developed in close connection with data from more than 60 experimental studies from the biology literature that illustrate the use of these results. This book is written for mathematicians and for biologists alike. We assume no previous knowledge of concepts from biology and only a basic knowledge of probability: a one semester undergraduate course and some familiarity with Markov chains and Poisson processes. Rick Durrett received his Ph.D. in operations research from Stanford University in 1976. He taught in the UCLA mathematics department before coming to Cornell in 1985. He is the author of six books and 125 research papers, and is the academic father of more than 30 Ph.D. students. His current interests are the use of probability models in genetics and ecology, and decreasing the mean and variance of his golf.
The Self Avoiding Walk
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Author : Neal Madras
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
The Self Avoiding Walk written by Neal Madras and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
A self-avoiding walk is a path on a lattice that does not visit the same site more than once. In spite of this simple definition, many of the most basic questions about this model are difficult to resolve in a mathematically rigorous fashion. In particular, we do not know much about how far an n step self-avoiding walk typically travels from its starting point, or even how many such walks there are. These and other important questions about the self-avoiding walk remain unsolved in the rigorous mathematical sense, although the physics and chemistry communities have reached consensus on the answers by a variety of nonrigorous methods, including computer simulations. But there has been progress among mathematicians as well, much of it in the last decade, and the primary goal of this book is to give an account of the current state of the art as far as rigorous results are concerned. A second goal of this book is to discuss some of the applications of the self-avoiding walk in physics and chemistry, and to describe some of the nonrigorous methods used in those fields. The model originated in chem istry several decades ago as a model for long-chain polymer molecules. Since then it has become an important model in statistical physics, as it exhibits critical behaviour analogous to that occurring in the Ising model and related systems such as percolation.