An extensive update to a classic text Stochastic geometry and spatial statistics play a
fundamental role in many modern branches of physics, materials sciences, engineering …

Based on a lecture course given at Chalmers University of Technology, this 2002 book is
ideal for advanced undergraduate or beginning graduate students. The author first develops …

Therandom-clustermodelwasinventedbyCees [Kees] FortuinandPietKasteleyn around 1969
as a uni? cation of percolation, Ising, and Potts models, and as an extrapolation of electrical …

We consider level-set percolation for the Gaussian free field on Z^ d, d≥ 3, and prove that,
as h varies, there is a non-trivial percolation phase transition of the excursion set above level …

This chapter is devoted to volume large deviation principles, as opposed to surface large
deviation principles. While the former are reminiscent of the case of iid random variables …

The paper considers spin systems on the d‐dimensional integer lattice ℤd with nearest‐
neighbor interactions. A sharp equivalence is proved between decay with distance of spin …

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 …

We present a new and simple approach to concentration inequalities in the context of
dependent random processes and random fields. Our method is based on coupling and …

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 …

We consider independent percolation, Ising and Potts models, and the contact process, on
infinite, locally finite, connected graphs. It is shown that on graphs with edge-isoperimetric …