The total mass of Brownian loop measure of Riemann surfaces for large genus

Jiankun Hou, Yunhui Wu

Let ${\mathcal{M}}_{g,n}(\mathbf{L})$ be the moduli space of hyperbolic surfaces of genus $g$ with $n\ge 0$ hyperbolic ends of widths $\mathbf{L}\in {\mathbb{R}}_{\ge 0}^n$. We reg…