arXiv subjects
Publications and source records attributed to Erik I. Broman.
In this paper we will investigate dynamic stability of percolation for the stochastic Ising model and the contact process. We also introduce the notion of downward and upward $ε$-movability which will be a key tool for our analysis.
In a recent paper by two of the authors, the concepts of upwards and downwards $ε$-movability were introduced, mainly as a technical tool for studying dynamical percolation of interacting particle systems. In this paper, we further explore these concepts which can be seen as refinements or quantifications of stochastic domination, and we relate them to previously studied concepts such as uniform insertion tolerance and extractability.
Given a trigonometric polynomial f:[0,1]\to[0,1] of degree m, one can define a corresponding stationary process {X_i}_{i\in Z} via determinants of the Toeplitz matrix for f. We show that for m=1 this process, which is trivially one-dependent, is a two-block-factor.