A new orbit closure in genus 8?
We provide numerical evidence that the orbit closure of the unfolding of the $(3,4,13)$-triangle is a previously unknown 4-dimensional variety.
math.DS↗
arXiv subjects
Delecroix Vincent
Publications and source records attributed to Delecroix Vincent.
Length partition of random multicurves on large genus hyperbolic surfaces
We study the length statistics of the components of a random multicurve on a surface of genus $g \geq 2$. For each fixed genus, the existence of such statistics follows from the work of M.~Mirzakhani, F.~Arana-Herrera and M.~Liu. We prove that as the genus $g$ tends to infinity the statistics converge in law to the Poisson--Dirichlet distribution of parameter $θ=1/2$. In particular, as the genus tends to infinity the mean length of the three longest components converge respectively to $75.8\%$, $17.1\%$ and $4.9\%$ of the total length.
math.GT↗