Book Review
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MathSciNet review:
3119829
Full text of review:
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Book Information:
Author:
Geoffrey Grimmett
Title:
Probability on graphs: random processes on graphs and lattices
Additional book information:
Institute of Mathematical Statistics Textbooks, Vol. 1,
Cambridge University Press,
Cambridge,
2010,
xii+247 pp.,
ISBN 978-0-521-14735-4,
US$38.99,
paperback
David Aldous, Interacting particle systems as stochastic social dynamics, Bernoulli (to appear, 2013).
David Aldous and James Fill, Reversible Markov chains and random walks on graphs, draft at http://www.stat.berkeley.edu/\textasciitilde aldous/RWG/book.html, 2002.
Claudio Castellano, Santo Fortunato, and Vittorio Loreto, Statistical physics of social dynamics, Rev. Mod. Phys., 81 (May 2009), 591–646.
Anna De Masi and Errico Presutti, Mathematical methods for hydrodynamic limits, Lecture Notes in Mathematics, vol. 1501, Springer-Verlag, Berlin, 1991. MR 1175626, DOI 10.1007/BFb0086457
Richard Durrett, Probability, The Wadsworth & Brooks/Cole Statistics/Probability Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1991. Theory and examples. MR 1068527
Rick Durrett, Ten lectures on particle systems, Lectures on probability theory (Saint-Flour, 1993) Lecture Notes in Math., vol. 1608, Springer, Berlin, 1995, pp. 97–201. MR 1383122, DOI 10.1007/BFb0095747
Massimo Franceschetti and Ronald Meester, Random networks for communication, Cambridge Series in Statistical and Probabilistic Mathematics, vol. 24, Cambridge University Press, Cambridge, 2007. From statistical physics to information systems. MR 2398551
Geoffrey Grimmett, Percolation, 2nd ed., Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 321, Springer-Verlag, Berlin, 1999. MR 1707339, DOI 10.1007/978-3-662-03981-6
Geoffrey Grimmett, The random-cluster model, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 333, Springer-Verlag, Berlin, 2006. MR 2243761, DOI 10.1007/978-3-540-32891-9
Fima C. Klebaner, Introduction to stochastic calculus with applications, 3rd ed., Imperial College Press, London, 2012. MR 2933773, DOI 10.1142/p821
David A. Levin, Yuval Peres, and Elizabeth L. Wilmer, Markov chains and mixing times, American Mathematical Society, Providence, RI, 2009. With a chapter by James G. Propp and David B. Wilson. MR 2466937, DOI 10.1090/mbk/058
Thomas M. Liggett, Interacting particle systems, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 276, Springer-Verlag, New York, 1985. MR 776231, DOI 10.1007/978-1-4613-8542-4
Thomas M. Liggett, Stochastic interacting systems: contact, voter and exclusion processes, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 324, Springer-Verlag, Berlin, 1999. MR 1717346, DOI 10.1007/978-3-662-03990-8
Marc Mézard and Andrea Montanari, Information, physics, and computation, Oxford Graduate Texts, Oxford University Press, Oxford, 2009. MR 2518205, DOI 10.1093/acprof:oso/9780198570837.001.0001
References
- David Aldous, Interacting particle systems as stochastic social dynamics, Bernoulli (to appear, 2013).
- David Aldous and James Fill, Reversible Markov chains and random walks on graphs, draft at http://www.stat.berkeley.edu/\textasciitilde aldous/RWG/book.html, 2002.
- Claudio Castellano, Santo Fortunato, and Vittorio Loreto, Statistical physics of social dynamics, Rev. Mod. Phys., 81 (May 2009), 591–646.
- Anna De Masi and Errico Presutti, Mathematical methods for hydrodynamic limits, Lecture Notes in Mathematics, vol. 1501, Springer-Verlag, Berlin, 1991. MR 1175626 (93k:60234)
- Richard Durrett, Probability: Theory and examples, The Wadsworth & Brooks/Cole Statistics/Probability Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1991. MR 1068527 (91m:60002)
- Rick Durrett, Ten lectures on particle systems, Lectures on probability theory (Saint-Flour, 1993) Lecture Notes in Math., vol. 1608, Springer, Berlin, 1995, pp. 97–201. MR 1383122 (97c:60236), DOI 10.1007/BFb0095747
- Massimo Franceschetti and Ronald Meester, Random networks for communication: from statistical physics to information systems, Cambridge Series in Statistical and Probabilistic Mathematics, Cambridge University Press, Cambridge, 2007. MR 2398551 (2009c:05221)
- Geoffrey Grimmett, Percolation, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 321, Springer-Verlag, Berlin, 1999. MR 1707339 (2001a:60114)
- Geoffrey Grimmett, The random-cluster model, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 333, Springer-Verlag, Berlin, 2006. MR 2243761 (2007m:60295), DOI 10.1007/978-3-540-32891-9
- Fima C. Klebaner, Introduction to stochastic calculus with applications, 3rd ed., Imperial College Press, London, 2012. MR 2933773
- David A. Levin, Yuval Peres, and Elizabeth L. Wilmer, Markov chains and mixing times (with a chapter by James G. Propp and David B. Wilson), American Mathematical Society, Providence, RI, 2009. MR 2466937 (2010c:60209)
- Thomas M. Liggett, Interacting particle systems, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 276, Springer-Verlag, New York, 1985. MR 776231 (86e:60089), DOI 10.1007/978-1-4613-8542-4
- Thomas M. Liggett, Stochastic interacting systems: contact, voter and exclusion processes, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 324, Springer-Verlag, Berlin, 1999. MR 1717346 (2001g:60247)
- Marc Mézard and Andrea Montanari, Information, physics, and computation, Oxford Graduate Texts, Oxford University Press, Oxford, 2009. MR 2518205 (2010k:94019), DOI 10.1093/acprof:oso/9780198570837.001.0001
Review Information:
Reviewer:
David Aldous
Affiliation:
University of California, Berkeley
Email:
aldous@stat.berkeley.edu
Journal:
Bull. Amer. Math. Soc.
51 (2014), 173-175
DOI:
https://doi.org/10.1090/S0273-0979-2013-01428-9
Published electronically:
July 26, 2013
Review copyright:
© Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
