Séminaire - Avril
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: avril.pdf.
- 13/04/2022 - Mingkun Liu (IMJ-PRG) - salle 01
Titre:
Length partition of random multi-geodesics on large genus hyperbolic
surfaces.
Resumé:Work
of Delecroix--Goujard--Zograf--Zorich showed that, a random
multi-geodesic on a hyperbolic surface is non-separating with high
probability as the genus g tends to infinity, and its number of
connected components is about log(g)/2. This talk aims to describe the
geometry of a random multi-geodesic in large genus hyperbolic surfaces.
More precisely, we will focus on the length partition, and we will see
that it converges in law to the Poisson--Dirichlet distribution of
parameter 1/2 as the genus goes to infinity. In particular, the average
lengths of the three largest components of a random multi-geodesic on a
large genus hyperbolic surface are approximately, 75.8%, 17.1%, and
4.9%, respectively, of the total length. This result further confirms
the intuition that, for large g, a random multi-geodesic on a
hyperbolic surface of genus g behaves like a random permutation of g
elements chosen according to the Ewens measure of parameter 1/2. This
is joint work with Vincent Delecroix.