相关论文: Matrix norms and rapid mixing for spin systems

In this paper we study the classic problem of computing a maximum cardinality matching in general graphs $G = (V, E)$. The best known algorithm for this problem till date runs in $O(m \sqrt{n})$ time due to Micali and Vazirani \cite{MV80}.…

Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and…

Let $T$ be a tree on $n$ vertices and with maximum degree $\Delta$. We show that for $k\geq \Delta+1$ the Glauber dynamics for $k$-edge-colourings of $T$ mixes in polynomial time in $n$. The bound on the number of colours is best possible…

A $k$-height on a graph $G=(V, E)$ is an assignment $V\to\{0, \ldots, k\}$ such that the value on ajacent vertices differs by at most $1$. We study the Markov chain on $k$-heights that in each step selects a vertex at random, and, if…

Peres and Winkler proved a "censoring" inequality for Glauber dynamics on monotone spins systems such as the Ising model. Specifically, if, starting from a constant-spin configuration, the spins are updated at some sequence of sites, then…

We study Glauber dynamics for sampling from discrete distributions $\mu$ on the hypercube $\{\pm 1\}^n$. Recently, techniques based on spectral independence have successfully yielded optimal $O(n)$ relaxation times for a host of different…

We study analytically and numerically the statics and the off-equilibrium dynamics of spin models over finitely connected random graphs. We identify a threshold value for the connectivity beyond which the loop structure of the graph becomes…

We consider the problem of computing expectation values of local functions under the Gibbs distribution of a spin system. In particular, we study two families of linear programming hierarchies for this problem. The first hierarchy imposes…

Learning maps between data samples is fundamental. Applications range from representation learning, image translation and generative modeling, to the estimation of spatial deformations. Such maps relate feature vectors, or map between…

Across many fields, a problem of interest is to predict the transition rates between nodes of a network, given limited stationary state and dynamical information. We give a solution using the principle of Maximum Caliber. We find the…

We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…

This paper extends the framework of randomised matrix multiplication to a coarser partition and proposes an algorithm as a complement to the classical algorithm, especially when the optimal probability distribution of the latter one is…

We introduce efficient algorithms for approximate sampling from symmetric Gibbs distributions on the sparse random (hyper)graph. The examples we consider include (but are not restricted to) important distributions on spin systems and…

Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…

We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest eigenvalue modulus of the transition…

We consider Metropolis Glauber dynamics for sampling proper $q$-colourings of the $n$-vertex complete $b$-ary tree when $3\leq q\leq b/2\ln(b)$. We give both upper and lower bounds on the mixing time. For fixed $q$ and $b$, our upper bound…

In this paper, we present a novel extension to the classical path coupling method to statistical mechanical models which we refer to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path…

We propose a simple modification of the density matrix renormalization group (DMRG) method in order to tackle strongly disordered quantum spin chains. Our proposal, akin to the idea of the adaptive time-dependent DMRG, enables us to reach…

Graph Neural Networks (GNNs) perform effectively when training and testing graphs are drawn from the same distribution, but struggle to generalize well in the face of distribution shifts. To address this issue, existing mainstreaming graph…

In this study, a versatile methodology for initiating polymerization from monomers in highly cross-linked materials is investigated. As polymerization progresses, force-field parameters undergo continuous modification due to the formation…