Analysis and Probability seminar

Motivated by Alain-Sol Sznitman's interlacement process, we consider the set of $\{0,1\}$-valued processes which can be constructed in an analogous way, namely as a union of sets coming from a  Poisson process on a collection of sets. Our main focus is to determine which processes are representable in this way. The models we consider include percolation, Markov chains, and the Ising model. This talk is based on joint work with Nina Gantert and Jeffrey E. Steif.