Random walk and the heat equation
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The work Random walk and the heat equation represents a distinct intellectual or artistic creation found in University of San Diego Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Random walk and the heat equation
Resource Information
The work Random walk and the heat equation represents a distinct intellectual or artistic creation found in University of San Diego Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Random walk and the heat equation
 Statement of responsibility
 Gregory F. Lawler
 Subject

 Measure and integration  Classical measure theory  Fractals
 Partial differential equations  Parabolic equations and systems  Heat equation
 Probability theory and stochastic processes  Instructional exposition (textbooks, tutorial papers, etc.)
 Probability theory and stochastic processes  Markov processes  Brownian motion
 Probability theory and stochastic processes  Stochastic processes  Martingales with discrete parameter
 Probability theory and stochastic processes  Stochastic processes  Sums of independent random variables; random walks
 Random walks (Mathematics)
 Heat equation
 Language
 eng
 Summary
 "The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective." "The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set." "The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas."BOOK JACKET
 Cataloging source
 DLC
 Illustrations
 illustrations
 Index
 no index present
 LC call number
 QA274.73
 LC item number
 .L39 2010
 Literary form
 non fiction
 Nature of contents
 bibliography
 Series statement
 Student mathematical library
 Series volume
 v. 55
Context
Context of Random walk and the heat equationWork of
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