The geometry of random minimal factorizations of a long cycle

27 October 2020
14:00
Igor Kortchemski

Further Information: 

Part of the Oxford Discrete Maths and Probability Seminar, held via Zoom. Please see the seminar website for details.

Abstract

We will be interested in the structure of random typical minimal factorizations of the n-cycle into transpositions, which are factorizations of $(1,\ldots,n)$ as a product of $n-1$ transpositions. We shall establish a phase transition when a certain amount of transpositions have been read one after the other. One of the main tools is a limit theorem for two-type Bienaymé-Galton-Watson trees conditioned on having given numbers of vertices of both types, which is of independent interest. This is joint work with Valentin Féray.

  • Combinatorial Theory Seminar