Stochastic domination: the contact process, Ising models and FKG measures☆

Stochastic Domination: the Contact Process, Ising Models and Fkg Measures

We prove for the contact process on Z, and many other graphs, that the upper invariant measure dominates a homogeneous product measure with large density if the infection rate λ is sufficiently large. As a consequence, this measure percolates if the corresponding product measure percolates. We raise the question of whether domination holds in the symmetric case for all infinite graphs of bounde...

Stochastic Domination for a Hidden Markov Chain with Applications to the Contact Process in a Randomly Evolving Environment

The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and study the contact process in a randomly evolving environment. Here we associate to every individual an independent two-state, {0,1}, background process. Giv...

Stochastic Geometry of Classical and Quantum Ising Models

Bipartition polynomials, the Ising model and domination in graphs

This paper introduces a trivariate graph polynomial that is a common generalization of the domination polynomial, the Ising polynomial, the matching polynomial, and the cut polynomial of a graph. This new graph polynomial, called the bipartition polynomial, permits a variety of interesting Research supported by ESF. Research supported by the Austrian National Research Network S11403-N23 (RiSE) ...

Stochastic Domination and Comb Percolation

There exists a Lipschitz embedding of a d-dimensional comb graph (consisting of infinitely many parallel copies of Z joined by a perpendicular copy) into the open set of site percolation on Z, whenever the parameter p is close enough to 1 or the Lipschitz constant is sufficiently large. This is proved using several new results and techniques involving stochastic domination, in contexts that inc...