Permutation Flip Processes

0583812 - ÚI 2024 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Hladký, Jan - Řada, Hanka
Permutation Flip Processes.
EUROCOMB’23. Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications. Brno: MUNI Press, 2023 - (Kráľ, D.; Nešetřil, J.), s. 587-594. E-ISSN 2788-3116.
[EUROCOMB 2023: European Conference on Combinatorics, Graph Theory and Applications /12./. Prague (CZ), 28.08.2023-01.09.2023]
Grant CEP: GA ČR(CZ) GX21-21762X
Institucionální podpora: RVO:67985807
Klíčová slova: permutation * permuton * sorting dynamics * flip process
Obor OECD: Pure mathematics
https://doi.org/10.5817/CZ.MUNI.EUROCOMB23-081

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.
Trvalý link: https://hdl.handle.net/11104/0351811