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We develop an efficient algorithmic approach for approximate counting and sampling in the low-temperature regime of a broad class of statistical physics models on finite subsets of the lattice $\mathbb Z^d$ and on the torus $(\mathbb Z/n…

Data Structures and Algorithms · Computer Science 2023-06-19 Tyler Helmuth , Will Perkins , Guus Regts

A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of…

Combinatorics · Mathematics 2015-07-14 Péter L. Erdős , István Miklós , Zoltán Toroczkai

We propose a new method called the Metropolis-adjusted Mirror Langevin algorithm for approximate sampling from distributions whose support is a compact and convex set. This algorithm adds an accept-reject filter to the Markov chain induced…

Computation · Statistics 2024-06-24 Vishwak Srinivasan , Andre Wibisono , Ashia Wilson

We present a randomized algorithm for solving low-degree polynomial equation systems over finite fields faster than exhaustive search. In order to do so, we follow a line of work by Lokshtanov, Paturi, Tamaki, Williams, and Yu (SODA 2017),…

Computational Complexity · Computer Science 2024-10-29 Holger Dell , Anselm Haak , Melvin Kallmayer , Leo Wennmann

We design an efficient sampling algorithm to generate samples from the hardcore model on random regular bipartite graphs as long as $\lambda \lesssim \frac{1}{\sqrt{\Delta}}$, where $\Delta$ is the degree. Combined with recent work of…

Data Structures and Algorithms · Computer Science 2026-04-24 Nicholas Kocurek , Shayan Oveis Gharan , Dante Tjowasi

In this paper we take inspiration from Weit'z algorithm for approximating the independence polynomial to provide a new algorithm for computing the coefficients of the Taylor series of the logarithm of the independence polynomial. Hereby we…

Data Structures and Algorithms · Computer Science 2025-09-26 Ferenc Bencs , Guus Regts

Abstract polymer models are systems of weighted objects, called polymers, equipped with an incompatibility relation. An important quantity associated with such models is the partition function, which is the weighted sum over all sets of…

Probability · Mathematics 2025-12-12 Tobias Friedrich , Andreas Göbel , Martin S. Krejca , Marcus Pappik

We discuss convergence and coupling of Markov chains, and present general relations between the transfer matrices describing these two processes. We then analyze a recently developed local-patch algorithm, which computes rigorous upper…

Statistical Mechanics · Physics 2013-05-29 Cedric Chanal , Werner Krauth

We describe a novel approach to accelerating Monte Carlo Markov Chains. Our focus is cosmological parameter estimation, but the algorithm is applicable to any problem for which the likelihood surface is a smooth function of the free…

Cosmology and Nongalactic Astrophysics · Physics 2015-05-20 Adam Bouland , Richard Easther , Katherine Rosenfeld

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…

Quantum Physics · Physics 2019-07-12 Ryan L. Mann , Michael J. Bremner

We propose a very fast approximate Markov Chain Monte Carlo (MCMC) sampling framework that is applicable to a large class of sparse Bayesian inference problems, where the computational cost per iteration in several models is of order…

Computation · Statistics 2021-08-17 Yves Atchadé , Liwei Wang

In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach…

Combinatorics · Mathematics 2018-01-11 Viresh Patel , Guus Regts

We present a Markov chain (Dikin walk) for sampling from a convex body equipped with a self-concordant barrier, whose mixing time from a "central point" is strongly polynomial in the description of the convex set. The mixing time of this…

Data Structures and Algorithms · Computer Science 2015-11-17 Hariharan Narayanan

We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems, one of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the…

Statistical Mechanics · Physics 2020-05-08 Fahim Faizi , George Deligiannidis , Edina Rosta

A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local…

Statistical Mechanics · Physics 2015-06-22 Jeremy Schofield , Hanif Bayat

A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are…

Quantum Physics · Physics 2022-03-18 A. Vourdas

This paper formalizes connections between stability of polynomials and convergence rates of Markov Chain Monte Carlo (MCMC) algorithms. We prove that if a (multivariate) partition function is nonzero in a region around a real point…

Data Structures and Algorithms · Computer Science 2024-08-07 Zongchen Chen , Kuikui Liu , Eric Vigoda

A wide class of ``counting'' problems have been studied in Computer Science. Three typical examples are the estimation of - (i) the permanent of an $n\times n$ 0-1 matrix, (ii) the partition function of certain $n-$ particle Statistical…

Probability · Mathematics 2007-05-23 Ravi Kannan

We consider the computational task of sampling a bit string $x$ from a distribution $\pi(x)=|\langle x|\psi\rangle|^2$, where $\psi$ is the unique ground state of a local Hamiltonian $H$. Our main result describes a direct link between the…

Quantum Physics · Physics 2023-11-09 Sergey Bravyi , Giuseppe Carleo , David Gosset , Yinchen Liu

We consider spin systems on general $n$-vertex graphs of unbounded degree and explore the effects of spectral independence on the rate of convergence to equilibrium of global Markov chains. Spectral independence is a novel way of…

Probability · Mathematics 2023-08-30 Antonio Blanca , Xusheng Zhang