DOI: 10.1007/s00440-004-0369-4. Glauber dynamics on trees and hyperbolic graphs

Glauber dynamics on trees and hyperbolic graphs

10.1007/s00440-004-0369-4

Crossref journal-article

Springer Science and Business Media LLC

Probability Theory and Related Fields (297)

Bibliography

Berger, N., Kenyon, C., Mossel, E., & Peres, Y. (2004). Glauber dynamics on trees and hyperbolic graphs. Probability Theory and Related Fields, 131(3), 311â340.

Authors 4

Noam Berger (first)
Claire Kenyon (additional)
Elchanan Mossel (additional)
Yuval Peres (additional)

References 37 Referenced 91

Aldous, D., Fill, J.A.: Reversible Markov chains and random walks on graphs. Book in preparation 2000, Current version available at http://www.stat.berkeley.edu/users/aldous/book.html
van den Berg, J.: A uniqueness condition for Gibbs measures, with application to the 2-dimensional Ising antiferromagnet. Comm. Math. Phys. 152 (1), 161–166 (1993) (10.1007/BF02097061) / Comm. Math. Phys. by Berg (1)
Bleher, P.M., Ruiz, J., Zagrebnov, V.A.: On the purity of limiting Gibbs state for the Ising model on the Bethe lattice. J. Stat. Phys 79, 473–482 (1995) (10.1007/BF02179399) / J. Stat. Phys by Bleher (1995)
Bubley, R., Dyer, M.: Path coupling: a technique for proving rapid mixing in Markov chains. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS), 1997, pp. 223–231
Chen, M.F.: Trilogy of couplings and general formulas for lower bound of spectral gap. Probability towards 2000, Lecture Notes in Statist., 128, Springer, New York, 1998, pp. 123–136 (10.1007/978-1-4612-2224-8_7)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York, 1991 (10.1002/0471200611)
Dyer, M., Greenhill, C.: On Markov chains for independent sets. J. Algor. 35, 17–49 (2000) (10.1006/jagm.1999.1071) / J. Algor. by Dyer (2000)
Evans, W., Kenyon, C., Peres, Y., Schulman, L.J.: Broadcasting on trees and the Ising Model. Ann. Appl. Prob. 10, 410–433 (2000) (10.1214/aoap/1019487349) / Ann. Appl. Prob. by Evans (2000)
Fortuin, C.M., Kasteleyn, P.W.: On the random-cluster model. I. Introduction and relation to other models. Physica 57, 536–564 (1972) / I. Introduction and relation to other models. Physica by Fortuin (1972)
Fortuin, C.M., Kasteleyn, P.W., Ginibre, J.: Correlation inequalities on some partially ordered sets. Comm. Math. Phys. 22, 89–103 (1971) (10.1007/BF01651330) / Comm. Math. Phys. by Fortuin (1971)
Haggstrom, O., Jonasson, J., Lyons, R.: Explicit isoperimetric constants and phase transitions in the random-cluster model. Ann. Probab. 30, 443–473 (2002) (10.1214/aop/1020107775) / Ann. Probab. by Haggstrom (2002)
Ioffe, D.: A note on the extremality of the disordered state for the Ising model on the Bethe lattice. Lett. Math. Phys. 37, 137–143 (1996) (10.1007/BF00416016) / Lett. Math. Phys. by Ioffe (1996)
Janson, S., Luczak, T., Ruciński, A.: Random Graphs. Wiley, New York, 2000 (10.1002/9781118032718)
Jerrum, M.: A very simple algorithm for estimating the number of k-colorings of a low-degree graph. Rand. Struc. Alg. 7, 157–165 (1995) (10.1002/rsa.3240070205) / Rand. Struc. Alg. by Jerrum (1995)
Jerrum, M., Sinclair, A.: Approximating the permanent. Siam J. Comput. 18, 1149–1178 (1989) (10.1137/0218077) / Siam J. Comput. by Jerrum (1989)
Jerrum, M., Sinclair, A.: Polynomial time approximation algorithms for the Ising model. Siam J. Comput. 22, 1087–1116 (1993) (10.1137/0222066) / Siam J. Comput. by Jerrum (1993)
Jerrum, M., Sinclair, A., Vigoda, E.: A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries. Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, Crete, Greece, 2001 (10.1145/380752.380877)
Katok, S.: Fuchsian Groups. University of Chicago Press, 1992
Kenyon, C., Mossel, E., Peres, Y.: Glauber dynamics on trees and hyperbolic graphs. 42nd IEEE Symposium on Foundations of Computer Science (Las Vegas, NV, 2001), IEEE Computer Soc., Los Alamitos, CA, 2001, pp. 568–578 (10.1109/SFCS.2001.959933)
Kinnersley, N.G.: The vertex seperation number of a graph equals its path-width. Infor. Proc. Lett. 42, 345–350 (1992) (10.1016/0020-0190(92)90234-M) / Infor. Proc. Lett. by Kinnersley (1992)
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Luby, M., Vigoda, E.: Fast Convergence of the Glauber Dynamics for Sampling Independent Sets, Statistical physics methods in discrete probability, combinatorics and theoretical computer science. Rand. Struc. Alg. 15, 229–241 (1999) (10.1002/(SICI)1098-2418(199910/12)15:3/4<229::AID-RSA3>3.0.CO;2-X) / Rand. Struc. Alg. by Luby (1999)
Magnus, W.: Noneuclidean tessellations and their groups. Academic Press, New York and London, 1974
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Martinelli, F., Sinclair, A., Weitz, D.: Glauber dynamics on trees: Boundary conditions and mixing time. Preprint 2003, available at http://front.math.ucdavis.edu/math.PR/0307336
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Mossel, E.: Recursive reconstruction on periodic trees. Rand. Struc. Alg. 13, 81–97 (1998) (10.1002/(SICI)1098-2418(199808)13:1<81::AID-RSA5>3.0.CO;2-O) / Rand. Struc. Alg. by Mossel (1998)
Mossel, E., Peres Y.: Information flow on trees. To appear in Ann. Appl. Probab., 2003 (10.1214/aoap/1060202828)
Nacu, S.: Glauber dynamics on the cycle is monotone. To appear, Probab. Theory Related Fields, 2003 (10.1007/s00440-003-0279-x)
Paterson, A.L.T.: Amenability. American Mathematical Soc., Providence, 1988 (10.1090/surv/029)
Propp, J., Wilson, D.: Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics. Rand. Struc. Alg. 9, 223–252 (1996) (10.1002/(SICI)1098-2418(199608/09)9:1/2<223::AID-RSA14>3.0.CO;2-O) / Rand. Struc. Alg. by Propp (1996)
Peres, Y., Winkler, P.: In preparation, 2003
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Robertson, N., Seymour, P.D.: Graph minors. I. Excluding a forest. J. Comb. Theory Series B 35, 39–61 (1983) (10.1016/0095-8956(83)90079-5) / I. Excluding a forest. J. Comb. Theory Series B by Robertson (1983)
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Dates

Type	When
Created	20 years, 7 months ago (Jan. 14, 2005, 3:01 p.m.)
Deposited	3 years, 3 months ago (May 9, 2022, 2:22 p.m.)
Indexed	2 months ago (June 21, 2025, 9:30 p.m.)
Issued	20 years, 7 months ago (Dec. 27, 2004)
Published	20 years, 7 months ago (Dec. 27, 2004)
Published Online	20 years, 7 months ago (Dec. 27, 2004)
Published Print	20 years, 5 months ago (March 1, 2005)

Funders 0

None

BibTeX

@article{Berger_2004, title={Glauber dynamics on trees and hyperbolic graphs}, volume={131}, ISSN={1432-2064}, url={http://dx.doi.org/10.1007/s00440-004-0369-4}, DOI={10.1007/s00440-004-0369-4}, number={3}, journal={Probability Theory and Related Fields}, publisher={Springer Science and Business Media LLC}, author={Berger, Noam and Kenyon, Claire and Mossel, Elchanan and Peres, Yuval}, year={2004}, month=dec, pages={311–340} }

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