Hanka Řada: Flip processes for permutations
In my talk, I will introduce a family of discrete-time stochastic processes on permutations, which we call flip processes. In these processes, at each step we sample a random fixed-size tuple from the domain and rearrange it according to a given rule.
I will show how the theory of permutons can be used to describe the typical evolution of such processes \(\pi_0, \pi_1, \pi_2, \dots\), starting from an arbitrary initial permutation \(\pi_0\). More specifically, we construct trajectories \(\Phi : \mathfrak{P} \times [0,\infty) \to \mathfrak{P}\) in the space of permutons \(\mathfrak{P}\) with the property that if \(\pi_0 \in S_n\) is close to a permuton \(\gamma\), then for any \(T > 0\), with high probability \(\pi_{T_n}\) is close to \(\Phi^T(\gamma)\).
This perspective allows us to study various questions inspired by dynamical systems.
This is a joint work with Jan Hladký.