Distribution of lengths of closed saddle connections on moduli space of large genus translation surface

Shenxing Zhang

Let $S_g$ be a closed surface of genus $g$ and ${\mathcal{H}}_g$ be the moduli space of Abelian differentials on $S_g$. A stratum of ${\mathcal{H}}_g$, endowed with the Masur-Veech mea…