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This paper formalizes connections between stability of polynomials and convergence rates of Markov Chain Monte Carlo (MCMC) algorithms.
“Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials”
Viresh Patel and Guus Regts · 1919
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“Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model”
Tsung-Dao Lee and Chen-Ning Yang · 1952
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“Theorems on the Partition Functions of the Heisenberg Ferromagnets”
Taro Asano · 1970
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“Extension of the Lee–Yang circle theorem”
David Ruelle · 1971
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“On the random-cluster model: I. Introduction and relation to other models”
Cornelius Fortuin and Piet Kasteleyn · 1972
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“Real and Complex Analysis”, Mathematics series
Walter Rudin · 1987
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“Approximating the Permanent”
Mark Jerrum and Alistair Sinclair · 1989
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“Polynomial-Time Approximation Algorithms for the Ising Model”
Mark Jerrum and Alistair Sinclair · 1993
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“Sampling spin configurations of an Ising system”
Dana Randall and David Wilson · 1999
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“Counting Independent Sets Up to the Tree Threshold”
Dror Weitz · 2006
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“Reconstruction for Models on Random Graphs”
Antoine Gerschenfeld and Andrea Montanari · 2007
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“Simulating Quantum Computation by Contracting Tensor Networks”
Igor. Markov and Yaoyun Shi · 2008
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“Weighted enumeration of spanning subgraphs with degree constraints”
David. Wagner · 2008
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“Sampling Edge Covers in 3-Regular Graphs”
Ivona Bezáková and William. Rummler · 2009
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“The Lee-Yang and Pólya-Schur programs. I. linear operators preserving stability”
Julius Borcea and Petter Brändén · 2009
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“Holant Problems and Counting CSP”
Jin-Yi Cai, Pinyan Lu and Mingji Xia · 2009
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“Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm”
Robert Edwards and Alan Sokal · 2009
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“Random even graphs”
Geoffrey Grimmett and Svante Janson · 2009
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“Quantum Computation and the Evaluation of Tensor Networks”
Itai Arad and Zeph Landau · 2010
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“Computational Complexity of Holant Problems”
Jin-Yi Cai, Pinyan Lu and Mingji Xia · 2011
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“From Holant to #CSP and back: Dichotomy for Holant c
Jin-Yi Cai, Sangxia Huang and Pinyan Lu · 2012
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“Approximating Holant problems by winding”
Colin McQuillan · 2013
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“A Simple FPTAS for Counting Edge Covers”
Chengyu Lin, Jingcheng Liu and Pinyan Lu · 2014
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“FPTAS for Counting Weighted Edge Covers”
Jingcheng Liu, Pinyan Lu and Chihao Zhang · 2014
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“The Ising partition function: Zeros and deterministic approximation”
Jingcheng Liu, Alistair Sinclair and Piyush Srivastava · 2019
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Vedat Alev and Lap Lau · 2020
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“Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model”
Nima Anari, Kuikui Liu and Shayan Oveis Gharan · 2020
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“Testing for Dense Subsets in a Graph via the Partition Function”
Alexander Barvinok and Anthony Della · 2020
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“Fractionally Log-Concave and Sector-Stable Polynomials: Counting Planar Matchings and More”
Yeganeh Alimohammadi, Nima Anari, Kirankumar Shiragur and Thuy-Duong Vuong · 2021
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“More on zeros and approximation of the Ising partition function”
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Román Orús · 2014
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“Computing the Partition Function for Cliques in a Graph”
Alexander Barvinok · 2015
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Alexander Barvinok and Pablo Soberón · 2015
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