Related papers: Spatial mixing and the random-cluster dynamics on …
Motivated by questions about the QCD deconfining phase transition, we studied in two previous papers Model A (Glauber) dynamics of 2D and 3D Potts models, focusing on structure factor evolution under heating (heating in the gauge theory…
We present a simple combinatorial framework for establishing approximate tensorization of variance and entropy in the setting of spin systems (a.k.a. undirected graphical models) based on balanced separators of the underlying graph. Such…
We show polylogarithmic mixing time bounds for the alternating-scan sampler for positively weighted restricted Boltzmann machines. This is done via analysing the same chain and the Glauber dynamics for ferromagnetic two-spin systems, where…
We prove that the continuous-time, single-flip Glauber dynamics for lozenge tilings of the size-$N$ hexagon mix in time $N^{2+o(1)}$. This was predicted to hold on fairly general domains of diameter $N$ (on the basis of the ``Lifshitz law''…
In this paper we investigate the relationship between the mixing times of the Glauber dynamics of a statistical mechanical system with its thermodynamic equilibrium structure. For this we consider the mean-field Blume-Capel model, one of…
Sufficiently strong inter-site interactions in extended-Hubbard and XXZ spin models result in dynamically-bound clusters at neighboring sites. We show that the dynamics of these clusters in two-dimensional lattices is remarkably different…
We study the mixing time of Glauber dynamics for Ising models in which the interaction matrix contains a single negative spectral outlier. This class includes the anti-ferromagnetic Curie-Weiss model, the anti-ferromagnetic Ising model on…
We consider the Glauber dynamics for model of polymer interacting with a substrate or wall. The state space is the set of one-dimensional nearest-neighbor paths on $\mathbb{Z}$ with nonnegative integer coordinates, starting at $0$ and…
The random-cluster model is a unifying framework for studying random graphs, spin systems and electrical networks that plays a fundamental role in designing efficient Markov Chain Monte Carlo (MCMC) sampling algorithms for the classical…
We study continuous time Glauber dynamics for random configurations with local constraints (e.g. proper coloring, Ising and Potts models) on finite graphs with $n$ vertices and of bounded degree. We show that the relaxation time (defined as…
The dynamics of heavy particles suspended in turbulent flows is of fundamental importance for a wide range of questions in astrophysics, atmospheric physics, oceanography, and technology. Laboratory experiments and numerical simulations…
We consider the phase ordering problem for the low-temperature Ising dynamics initialized from a biased and disordered initialization. Work of Fontes, Schonmann, Sidoravicius (2002) showed that at zero-temperature, Ising Glauber dynamics on…
We study the stochastic Ising model on finite graphs with n vertices and bounded degree and analyze the effect of boundary conditions on the mixing time. We show that for all low enough temperatures, the spectral gap of the dynamics with…
We consider the Potts model on a two-dimensional periodic rectangular lattice with general coupling constants $J_{ij}>0$, where $i,j\in\{1,2,3\}$ are the possible spin values (or colors). The resulting energy landscape is thus significantly…
We study the random-cluster model on trees and treelike graphs at low temperatures. This is a model of dependent percolation parametrized by an edge probability $p\in (0,1)$ and a clustering weight $q\in [1,\infty)$, generalizing…
Masked language models (MLMs) define local conditional distributions over tokens but do not, in general, correspond to any consistent joint distribution over sequences. This raises a fundamental question: what global distributional behavior…
This paper provides an overview of the research on the metastable behavior of the Ising model. We analyze the transition times from the set of metastable states to the set of the stable states by identifying the critical configurations that…
We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…
The effect of initial spin configurations on zero-temperature Glauber spin dynamics in complex networks is investigated. In a system in which the initial spins are defined by centrality measures at the vertices of a network, a variety of…
Consider the event that there is a $+$ crossing from left to right in a box for the Ising model on the triangular lattice. We show that this event is noise sensitive under Glauber dynamics $t \mapsto \sigma_t$ in the subcritical regime…