Encyclopaedia of Mathematical Sciences Probability Theory

Probability on Discrete Structures

Editors: Kesten, Harry (Ed.)

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About this book

Most probability problems involve random variables indexed by space and/or time. These problems almost always  have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery.
The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks.
The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.

Reviews

From the reviews:

"The ... book contains five survey articles which span a very nice part of modern discrete probability theory. … The world of discrete probability theory seems to be growing at an exponential rate and it is exactly for this reason that such surveys are not only welcome but essential. Each one of these articles is indeed very interesting and both the ‘beginner’ … and the expert can learn a tremendous amount. In short, it is a wonderful book and to be recommended." (Jeffrey E. Steif, Combinatorics, Probability and Computing, Vol. 14, 2005)

"This book covers probability problems with random variables whose indices take discrete values. The exposition is very clear and the book provides an introduction to the subject and to the mathematical formalism which is used. Each chapter is on a different topic, and it represents a clear, rather complete review of the state of the art of its own subject." (Guido Gentile, SIAM Review, Vol. 47 (3), 2005)


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook 93,08 €
price for Spain (gross)
  • ISBN 978-3-662-09444-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-3-540-00845-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,95 €
price for Spain (gross)
  • ISBN 978-3-642-05647-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Probability on Discrete Structures
Editors
  • Harry Kesten
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
110
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-09444-0
DOI
10.1007/978-3-662-09444-0
Hardcover ISBN
978-3-540-00845-3
Softcover ISBN
978-3-642-05647-5
Series ISSN
0938-0396
Edition Number
1
Number of Pages
IX, 351
Topics