We study continuous time Glauber dynamics for random configurations with local constraints
(eg proper coloring, Ising and Potts models) on finite graphs with n vertices and of bounded …

Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation
Introduction Page 1 Math. Model. Nat. Phenom. Vol. 5, No. 2, 2010, pp. 198-224 DOI …

The class of random-cluster models is a unification of a variety of stochastic processes of
significance for probability and statistical physics, including percolation, Ising, and Potts …

This paper is an up-to-date introduction to the problem of uniqueness versus non-
uniqueness of infinite clusters for percolation on ℤ d and, more generally, on transitive …

Cheeger inequalities for unbounded graph Laplacians Page 1 DOI 10.4171/JEMS/503 J. Eur.
Math. Soc. 17, 259–271 c European Mathematical Society 2015 Frank Bauer · Matthias Keller …

The main focus in this memoir is on Laplacians on both weighted graphs and weighted
metric graphs. Let us emphasize that we consider infinite locally finite graphs and do not …

We prove that at any inverse temperature β and on any transitive amenable graph, the
automorphism-invariant Gibbs states of the ferromagnetic Ising model are convex …

The main goal of this paper is to answer Question 1.10 and settle Conjecture 1.11 of
Benjamini–Lyons–Schramm [BenLS] relating harmonic Dirichlet functions on a graph to …

We introduce a curvature function for planar graphs to study the connection between the
curvature and the geometric and spectral properties of the graph. We show that non-positive …

Let G ¼ šVšGŽ; EšGŽŽ be a connected undirected graph without loops and multiple edges,
where VšGŽ is the set of vertices and EšGŽ is the set of edges. For x 2 VšGŽ, the degree of x …