Next Monday (26th April) at 11am (UK time) there’ll be an online probability seminar given by Vladislav Vysotskiy.

Title: How long is the convex minorant of a one-dimensional random walk?

Abstract: We prove distributional limit theorems for the length of the largest convex minorant of a one dimensional random walk with independent identically distributed increments. Depending on the distribution of the increments there are several regimes with different limit distributions for the length. The most prominent of our results is a central limit theorem for the length in the case when the increments have zero mean and finite variance. Among other tools, we employ a representation of convex minorants of random walks in terms of uniform random permutations. This talk is based on a joint work with Gerold Alsmeyer, Zakhar Kabluchko, and Alexander Marynych.