Abstract: A factorization of the cycle (1, ..., n) is a way to write it as a product of a given number m of transpositions. When m is fixed, such a factorization can be coded by a graph on a torus, whose genus
only depends on m. We first obtain an explicit (almost) bijection between these factorizations and these graphs, which allows us to algorithmically sample a uniform factorization of given genus. In a second time, we use this bijection to define and characterize the scaling limit of a uniform factorization, when the genus is fixed and the size n grows.
Joint work with Valentin Féray and Baptiste Louf
Asymptotic bijection and scaling limits for factorizations of a long cycle
25.05.2023 14:00 - 16:00
Organiser:
M. Lis
Location: