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 …

We present a detailed probabilistic and structural analysis of the set of weighted
homomorphisms from the discrete torus Z mn, where m is even, to any fixed graph: we show …

We establish a refined version of a graph container lemma due to Galvin and discuss
several applications related to the hard-core model on bipartite expander graphs. Given a …

In this paper we study sum-free sets of order m in finite abelian groups. We prove a general
theorem about independent sets in 3-uniform hypergraphs, which allows us to deduce …

We prove tight bounds on the site percolation threshold for $ k $-uniform hypergraphs of
maximum degree $\Delta $ and for $ k $-uniform hypergraphs of maximum degree $\Delta …

We establish long-range order for discrete nearest-neighbor spin systems on $\mathbb {Z}^
d $ satisfying a certain symmetry assumption, when the dimension $ d $ is higher than an …

It has been shown by van den Berg and Steif (Ann. Probab. 27 (1999) 1501–1522) that the
subcritical and critical Ising model on Z^d is a finitary factor of an iid process (ffiid), whereas …

A proper q-coloring of a domain in Z d is a function assigning one of q colors to each vertex
of the domain such that adjacent vertices are colored differently. Sampling a proper q …

A proper $ q $-coloring of a domain in $\mathbb {Z}^ d $ is a function assigning one of $ q $
colors to each vertex of the domain such that adjacent vertices are colored differently …

We consider the hard‐core model on finite triangular lattices with Metropolis dynamics.
Under suitable conditions on the triangular lattice sizes, this interacting particle system has 3 …