Probability on Discrete Structures by D. Aldous, G.R. Grimmett, C.D. Howard


Probability on Discrete Structures by D. Aldous, G.R. Grimmett, C.D. Howard

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.


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)

About the Author

Other Formats

Book Info


360 pages


D. Aldous, G.R. Grimmett, C.D. Howard
More books by D. Aldous, G.R. Grimmett, C.D. Howard


Publication date

18th September 2003



Lovereading4kids is great, we get books really early never late. We love to read and review, and think you would like it too. The excitement

Jasmine Harris-Hart, age 12

I love ‘LoveReading 4 kids’ because they let you read and learn things you’d never dreamed of learning before.

Emily Horncastle – age 11

It gives me a chance to read types of books that I would not normally try, and it motivates me to read every night to finish it!

Alice Horncastle, age 14

We love Lovereading as my 5 year old loves to read new books before anyone else has a chance, she says it makes reading exciting!

Tracey Chorley

We love Lovereading4kids because they put books in front of us we wouldn’t otherwise have read. They make us more adventurous readers!

Emily Jacques

I am so pleased to have signed my kids up as they are reading a much wider range of books and even choosing books out of their comfort zone.

Angela East

I love all the books they recommend & put up for me to review. I also love the fact that they give new authors the chance to share their boo

Daisy Pennock – age 15

I think Lovereading4kids is an amazing company because of the friendly staff and the fabulous chance to read great books before publication.

Adam Graham

Lovereading 4 schools