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.