Random Walk: A Modern Introduction

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Cambridge University Press, Jun 24, 2010 - Mathematics
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.
 

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Contents

A MODERN INTRODUCTION 1 Introduction
1
A MODERN INTRODUCTION 2 Local central limit theorem
21
A MODERN INTRODUCTION 3 Approximation by Brownian motion
72
A MODERN INTRODUCTION 4 The Greens function
87
A MODERN INTRODUCTION 5 Onedimensional walks
123
A MODERN INTRODUCTION 6 Potential theory
144
A MODERN INTRODUCTION 7 Dyadic coupling
205
A MODERN INTRODUCTION 8 Additional topics on simple random walk
225
A MODERN INTRODUCTION 9 Loop measures
247
A MODERN INTRODUCTION 10 Intersection probabilities for random walks
297
A MODERN INTRODUCTION 11 Looperased random walk
307
A MODERN INTRODUCTION Appendix
326
A MODERN INTRODUCTION Bibliography
360
A MODERN INTRODUCTION Index of Symbols
361
A MODERN INTRODUCTION Index
363
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About the author (2010)

Gregory F. Lawler is Professor of Mathematics and Statistics at the University of Chicago. He received the George Pólya Prize in 2006 for his work with Oded Schramm and Wendelin Werner.

Vlada Limic works as a researcher for Centre National de la Recherche Scientifique (CNRS) at Université de Provence, Marseilles.