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We say a probability distribution $\mu$ is spectrally independent if an associated correlation matrix has a bounded largest eigenvalue for the distribution and all of its conditional distributions.
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“Completely Analytical Gibbs Fields”
R.. Dobrushin and S.. Shlosman · 1985
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“Constructive Criterion for the Uniqueness of Gibbs Field”
R.. Dobrushin and S.. Shlosman · 1985
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“Stochastic Models of Computer Communication Systems”
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R.. Dobrushin and S.. Shlosman · 1987
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“Approximating the Permanent”
M. Jerrum and Alistair Sinclair · 1989
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“Geometric bounds for eigenvalues of Markov chains”
Persi Diaconis and Daniel Stroock · 1991
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“Balanced matroids”
Tomás Feder and Milena Mihail · 1992
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Salil. Vadhan · 1995
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“Approximately Counting Up to Four (Extended Abstract)”
Michael Luby and Eric Vigoda · 1997
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“Fast convergence of the Glauber dynamics for sampling independent sets”
Michael Luby and Eric Vigoda · 1999
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“On Markov Chains for Independent Sets”
Martin Dyer and Catherine Greenhill · 2000
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“The complexity of counting colourings and independent sets in sparse graphs and hypergraphs”
Catherine. Greenhill · 2000
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“Determinants of Block Matrices”
John. Silvester · 2000
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“A Note on the Glauber Dynamics for Sampling Independent Sets”
Eric Vigoda · 2001
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“On Counting Independent Sets in Sparse Graphs”
Martin Dyer, Alan Frieze and Mark Jerrum · 2002
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“Mixing in Time and Space for Lattice Spin Systems: A Combinatorial View”
Martin Dyer, Alistair Sinclair, Eric Vigoda and Dror Weitz · 2002
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“The Complexity of Counting in Sparse, Regular, and Planar Graphs”
Salil. Vadhan · 2002
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“The computational complexity of two‐state spin systems”
Leslie Goldberg, Mark Jerrum and Mike Paterson · 2003
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“The Ising model on trees: boundary conditions and mixing time”
F. Martinelli, A. Sinclair and D. Weitz · 2003
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“Fast Mixing for Independent Sets, Colorings and Other Models on Trees”
Fabio Martinelli, Alistair Sinclair and Dror Weitz · 2004
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“Mixing in Time and Space for Discrete Spin Systems” AAI3147046
Dror Weitz · 2004
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“Coupling with the Stationary Distribution and Improved Sampling for Colorings and Independent Sets”
Tom Hayes and Eric Vigoda · 2005
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Alexander. Scott and Alan. Sokal · 2005
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“A simple condition implying rapid mixing of single-site dynamics on spin systems”
Thomas. Hayes · 2006
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“Counting Independent Sets Up to the Tree Threshold”
Dror Weitz · 2006
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Mohsen Bayati, David Gamarnik, Dimitriy Katz, Chandra Nair and Prasad Tetali · 2007
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“Correlation Decay and Deterministic FPTAS for Counting List-colorings of a Graph”
“Inapproximability for Antiferromagnetic Spin Systems in the Tree Nonuniqueness Region”
Andreas Galanis, Daniel Štefankovič and Eric Vigoda · 2015
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“Spatial Mixing and the Connective Constant: Optimal Bounds”
Alistair Sinclair, Piyush Srivastava, Daniel Štefankovič and Yitong Yin · 2015
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“Monte Carlo Markov Chain Algorithms for Sampling Strongly Rayleigh Distributions and Determinantal Point Processes” 49
Nima Anari, Shayan Gharan and Alireza Rezaei · 2016
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“Combinatorics and Complexity of Partition Functions”
Alexander Barvinok · 2016
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“Computing the Permanent of (Some) Complex Matrices”
Alexander Barvinok · 2016
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“Convergence of MCMC and Loopy BP in the Tree Uniqueness Region for the Hard-Core Model”
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David Gamarnik and Dmitriy Katz · 2007
Cited alongside, same era.
“On the hardness of sampling independent sets beyond the tree threshold”
Elchanan Mossel, Dror Weitz and Nicholas. Wormald · 2007
Cited alongside, same era.
“Counting Without Sampling: Asymptotics of the Log-partition Function for Certain Statistical Physics Models”
Antar Bandyopadhyay and David Gamarnik · 2008
Cited alongside, same era.
“Rapid Mixing of Gibbs Sampling on Graphs That Are Sparse on Average”
Elchanan Mossel and Allan Sly · 2008
Cited alongside, same era.
“Matrix Norms and Rapid Mixing for Spin Systems”
Martin Dyer, Leslie Goldberg and Mark Jerrum · 2009
Cited alongside, same era.
“Computational Transition at the Uniqueness Threshold”
Allan Sly · 2010
Cited alongside, same era.
“Counting Independent Sets Using the Bethe Approximation”
Venkat Chandrasekaran, Misha Chertkov, David Gamarnik, Devavrat Shah and Jinwoo Shin · 2011
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Charilaos Efthymiou, Thomas. Hayes, Daniel Štefankovič, Eric Vigoda and Yitong Yin · 2016
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“Inapproximability of the Partition Function for the Antiferromagnetic Ising and Hard-Core Models”
Andreas Galanis, Daniel Štefankovič and Eric Vigoda · 2016
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“High Dimensional Expanders Imply Agreement Expanders”
I. Dinur and T. Kaufman · 2017
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“High Dimensional Random Walks and Colorful Expansion”
Tali Kaufman and David Mass · 2017
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“Computing the Independence Polynomial: From the Tree Threshold Down to the Roots”
Nicholas.. Harvey, Piyush Srivastava and Jan Vondrák · 2018
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“High Order Random Walks: Beyond Spectral Gap”
Tali Kaufman and Izhar Oppenheim · 2018
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“Local spectral expansion approach to high dimensional expanders part I: Descent of spectral gaps”
Izhar Oppenheim · 2018
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“Log-Concave Polynomials II: High-Dimensional Walks and an FPRAS for Counting Bases of a Matroid”
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“Phase Coexistence for the Hard-Core Model on ℤ 2 \mathbb{Z}^{2} ”
Antonio Blanca, Yuxuan Chen, David Galvin, Dana Randall and Prasad Tetali · 2019
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“Approximate counting, phase transitions and geometry of polynomials”, 2019
Jingcheng Liu · 2019
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“Fisher zeros and correlation decay in the Ising model”
Jingcheng Liu, Alistair Sinclair and Piyush Srivastava · 2019
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“On a conjecture of Sokal concerning roots of the independence polynomial”
Han Peters and Guus Regts · 2019
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“Contraction: a Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems”
Shuai Shao and Yuxin Sun · 2019
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“Improved Analysis of Higher Order Random Walks and Applications”
Vedat Alev and Lap Lau · 2020
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Antonio Blanca, Zongchen Chen and Eric Vigoda · 2020
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Zongchen Chen, Kuikui Liu and Eric Vigoda · 2020
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“Rapid mixing from spectral independence beyond the Boolean domain”
Weiming Feng, Heng Guo, Yitong Yin and Chihao Zhang · 2020
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