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Universität Augsburg
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Universität Augsburg
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Amanda Priestley
Austin, Texas
spricht am
Mittwoch, 10. Juni 2026
um
10:30 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| The set of parking functions of length $n$ is a generalization of the symmetric group on $n$ elements, first introduced by Konheim and Weiss in 1966. While much is known about these objects from an enumerative combinatorics perspective, far less is known from a probabilistic perspective. In this work, we give definitions of \textit{fast} and \textit{slow} single site dynamics for sampling uniformly from the set of parking functions, and compare the Mixing times of these processes to the analogous process on the full space $[n]^n$. As far as we are aware, these are the first Markov chains to be defined that act directly on the set of parking functions, rather than sampling by way of a bijection. Moreover, as the set of parking functions forms a monotone subset of $[n]^n$, determining the mixing time of these processes has interesting implications for the theory of Markov chain mixing, and more specifically, the cutoff phenomenon. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Dominik Schmid |