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Random walk and the heat equation (Record no. 36064)

MARC details
000 -LEADER
fixed length control field 02938nam a22002657a 4500
003 - CONTROL NUMBER IDENTIFIER
control field OSt
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20250617095231.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 250616b |||||||| |||| 00| 0 hin d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9789349750630
040 ## - CATALOGING SOURCE
Original cataloging agency NISER LIBRARY
Language of cataloging eng
Transcribing agency NISER LIBRARY
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 519.2
Item number LAW-R
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Lawler, Gregory F.
245 ## - TITLE STATEMENT
Title Random walk and the heat equation
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc. India :
Name of publisher, distributor, etc. Universities Press,
Date of publication, distribution, etc. 2025.
300 ## - PHYSICAL DESCRIPTION
Extent ix, 156 p. :
Other physical details ill. ;
Dimensions 22 cm.
490 ## - SERIES STATEMENT
Series statement Student mathematical library ;
Volume/sequential designation v. 55
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references.
520 ## - SUMMARY, ETC.
Summary, etc. 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 by 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 equation and the closely related notion of harmonic functions from a probabilistic perspective.<br/><br/>The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The 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.<br/><br/>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.
521 ## - TARGET AUDIENCE NOTE
Target audience note Readership: Undergraduate students interested in probability and connections between probability and classical analysis.
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Random walks (Mathematics)
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Heat equation
856 ## - ELECTRONIC LOCATION AND ACCESS
Materials specified Table of Contents
Uniform Resource Identifier <a href="https://www.ams.org/bookstore/pspdf/stml-55-toc.pdf?_gl=1*ygvj0b*_ga*NzkyMDE0ODczLjE3NTAwNDYzMjU.*_ga_26G4XFTR63*czE3NTAxMzI2MzckbzIkZzEkdDE3NTAxMzM3MjEkajUyJGwwJGgw">https://www.ams.org/bookstore/pspdf/stml-55-toc.pdf?_gl=1*ygvj0b*_ga*NzkyMDE0ODczLjE3NTAwNDYzMjU.*_ga_26G4XFTR63*czE3NTAxMzI2MzckbzIkZzEkdDE3NTAxMzM3MjEkajUyJGwwJGgw</a>
856 ## - ELECTRONIC LOCATION AND ACCESS
Materials specified Reviews
Uniform Resource Identifier <a href="https://www.goodreads.com/book/show/11261817-random-walk-and-the-heat-equation-student-mathematical-library?ref=nav_sb_ss_1_33#CommunityReviews">https://www.goodreads.com/book/show/11261817-random-walk-and-the-heat-equation-student-mathematical-library?ref=nav_sb_ss_1_33#CommunityReviews</a>
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Universal Decimal Classification
Koha item type NBHM Books
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Home library Current library Date acquired Total Checkouts Full call number Barcode Date last seen Price effective from Koha item type
    Universal Decimal Classification     SMS Library SMS Library 12/06/2025   519.2 LAW-R N484 16/06/2025 16/06/2025 NBHM Books
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