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Permutation Flip Processes
 Hladký, Jan ; Řada, Hanka
We introduce a broad class of stochastic processes on permutations which we call flip processes. A single step in these processes is given by a local change on a randomly chosen fixed-sized tuple of the domain. We use the theory of permutons to describe the typical evolution of any such flip process started from any initial permutation. More specifically, we construct trajectories in the space of permutons with the property that if a finite permutation is close to a permuton then for any time it stays with high probability is close to this predicted trajectory. This view allows to study various questions inspired by dynamical systems.
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