DOI: 10.1002/rsa.20073. Combinatorial criteria for uniqueness of Gibbs measures

Combinatorial criteria for uniqueness of Gibbs measures

10.1002/rsa.20073

Crossref journal-article

Wiley

Random Structures & Algorithms (311)

Abstract

AbstractWe generalize previously known conditions for uniqueness of the Gibbs measure in statistical physics models by presenting conditions of any finite size for models on any underlying graph. We give two dual conditions, one requiring that the total influenceona site is small, and the other that the total influenceofa site is small. Our proofs are combinatorial in nature and use tools from the analysis of discrete Markov chains, in particular the path coupling method. The implications of our conditions for the mixing time of natural Markov chains associated with the models are discussed as well. We also present some examples of models for which the conditions hold. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005

Bibliography

Weitz, D. (2005). Combinatorial criteria for uniqueness of Gibbs measures. Random Structures & Algorithms, 27(4), 445â475. Portico.

Authors 1

Dror Weitz (first)

References 22 Referenced 46

N.Berger C.Kenyon E.Mossel andY.Peres Glauber dynamics on trees and hyperbolic graphs preprint 2003. (10.1007/s00440-004-0369-4)
For a short version seeC.Kenyon E.Mossel andY.Peres Glauber dynamics on trees and hyperbolic graphs Proc 42nd IEEE Symp Foundations of Computer Science 2001 pp.568–578. (10.1109/SFCS.2001.959933)
R.BubleyandM. E.Dyer Path coupling: A technique for proving rapid mixing in Markov chains Proc 38th IEEE Symp Foundations of Computer Science 1997 pp.223–231. (10.1109/SFCS.1997.646111)
10.1007/PL00008792
10.1137/1115049
10.1007/978-1-4899-6653-7_20
10.1007/978-1-4899-6653-7_21
10.1006/jagm.1999.1071
10.1002/rsa.20004
10.1515/9783110850147
{'key': 'e_1_2_1_11_2', 'series-title': 'Phase transitions and critical phenomena', 'first-page': '1', 'author': 'Georgii H.‐O.', 'year': '2001'} / Phase transitions and critical phenomena by Georgii H.‐O. (2001)
10.1016/S0167-7152(02)00054-8
10.1007/BF01016786
{'key': 'e_1_2_1_14_2', 'series-title': 'Lecture Notes in Mathematics', 'first-page': '93', 'volume-title': 'Lectures on probability theory and statistics (Saint‐Flour, 1997)', 'author': 'Martinelli F.', 'year': '1998'} / Lectures on probability theory and statistics (Saint‐Flour, 1997) / Lecture Notes in Mathematics by Martinelli F. (1998)
10.1007/BF02101929
10.1007/s00220-004-1147-y
F.Martinelli A.Sinclair andD.Weitz “Fast mixing for independent sets colorings and other models on trees Proc 15th ACM‐SIAM Symp Discrete Algorithms (SODA) January2004 pp.456–465.
10.1017/CBO9780511897122
10.1007/BF02199113
10.1007/BFb0092621
10.1007/BF02096629
E.Vigoda Improved bounds for sampling colorings Proc 40th IEEE Symp Foundations of Computer Science 1999 pp.51–59. (10.1109/SFFCS.1999.814577)

Dates

Type	When
Created	20 years, 3 months ago (May 24, 2005, 3:09 p.m.)
Deposited	8 months ago (Jan. 1, 2025, 4:58 a.m.)
Indexed	4 months, 3 weeks ago (April 9, 2025, 12:50 p.m.)
Issued	20 years, 3 months ago (May 24, 2005)
Published	20 years, 3 months ago (May 24, 2005)
Published Online	20 years, 3 months ago (May 24, 2005)
Published Print	19 years, 9 months ago (Dec. 1, 2005)

Funders 0

None

BibTeX

@article{Weitz_2005, title={Combinatorial criteria for uniqueness of Gibbs measures}, volume={27}, ISSN={1098-2418}, url={http://dx.doi.org/10.1002/rsa.20073}, DOI={10.1002/rsa.20073}, number={4}, journal={Random Structures & Algorithms}, publisher={Wiley}, author={Weitz, Dror}, year={2005}, month=may, pages={445–475} }

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