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We give a complete characterization of the two-state anti-ferromagnetic spin systems which are of strong spatial mixing on general graphs.
Stochastic models of computer communication systems
F. Kelly · 1985
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Polynomial-time approximation algorithms for the ising model
M. Jerrum and A. Sinclair · 1993
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A very simple algorithm for estimating the number of k-colorings of a low-degree graph
M. Jerrum · 1995
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Approximately counting up to four (extended abstract)
M. Luby and E. Vigoda · 1997
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Improved bounds for sampling coloring
E. Vigoda · 1999
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On markov chains for independent sets
M. E. Dyer and C. S. Greenhill · 2000
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Rapidly mixing markov chains for dismantleable constraint graphs
M. Dyer, M. Jerrum, and E. Vigoda · 2001
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On counting independent sets in sparse graphs
M. E. Dyer, A. M. Frieze, and M. Jerrum · 2002
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The computational complexity of two-state spin systems
L. A. Goldberg, M. Jerrum, and M. Paterson · 2003
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A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
M. Jerrum, A. Sinclair, and E. Vigoda · 2004
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Counting independent sets up to the tree threshold
D. Weitz · 2006
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Simple deterministic approximation algorithms for counting matchings
M. Bayati, D. Gamarnik, D. Katz, C. Nair, and P. Tetali · 2007
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Correlation decay and deterministic fptas for counting list-colorings of a graph
D. Gamarnik and D. Katz · 2007
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Fast mixing for independent sets, colorings, and other models on trees
F. Martinelli, A. Sinclair, and D. Weitz · 2007
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Counting without sampling: Asymptotics of the log-partition function for certain statistical physics models
Improved inapproximability results for counting independent sets in the hard-core model
A. Galanis, Q. Ge, D. Štefankovič, E. Vigoda, and L. Yang · 2011
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A polynomial-time algorithm for estimating the partition function of the ferromagnetic ising model on a regular matroid
L. A. Goldberg and M. Jerrum · 2011
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Improved mixing condition on the grid for counting and sampling independent sets
R. Restrepo, J. Shin, P. Tetali, E. Vigoda, and L. Yang · 2011
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Inapproximability of the partition function for the antiferromagnetic ising and hard-core models
A. Galanis, D. Stefankovic, and E. Vigoda · 2012
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Approximate counting via correlation decay in spin systems
L. Li, P. Lu, and Y. Yin · 2012
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A. Bandyopadhyay and D. Gamarnik · 2008
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Uniqueness thresholds on trees versus graphs
A. Sly · 2008
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On the hardness of sampling independent sets beyond the tree threshold
E. Mossel, D. Weitz, and N. Wormald · 2009
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Computational transition at the uniqueness threshold
A. Sly · 2010
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Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs
A. Sinclair, P. Srivastava, and M. Thurley · 2012
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The computational hardness of counting in two-spin models on d-regular graphs
A. Sly and N. Sun · 2012
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Correlation Decay up to Uniqueness in Spin Systems
L. Li, P. Lu, and Y. Yin · 2013
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