[STAT/AP] Carla Groenland: Counting graphic sequences via integrated random walks

02 October 2023 15:45 till 16:45 - Location: Lecture Hall G | Add to my calendar

Via a new probabilistic result, we provide (1+o(1))-asymptotics for the number of integer sequences n-1>= d_1 >= ... >= d_n >= 0 that form the degree sequence of an n-vertex graph (improving both the upper and lower bound by a multiplicative n^{1/4}-factor).  In particular, we determine the asymptotic probability that the integral of a (lazy) simple symmetric random walk bridge remains non-negative. This talk will explain how this problem arose, what the connection is with the problem about random walks (including what all the words in this abstract mean) and then provide a short sketch of the proof. This is based on joint work with Paul Balister, Serte Donderwinkel, Tom Johnston and Alex Scott.