Care colleghe e colleghi,
vi invio l'annuncio del seminario di Vladislav Vysotskiy il 26 aprile a
mezzogiorno. Le persone interessate possono ottenere il link contattando
l'organizzatrice, Dr Minmin Wang (minmin.wang(a)sussex.ac.uk).
Cordiali saluti,
Enrico Scalas
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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.