Brownian loops on non-smooth surfaces and the Polyakov-Alvarez formula

Minjae Park, Joshua Pfeffer, Scott Sheffield

Let $\rho$ be compactly supported on $D\subset {\mathbb{R}}^2$. Endow ${\mathbb{R}}^2$ with the metric $e^{\rho }(d{x}_1^2+d{x}_2^2)$. As $\delta \to 0$ the set of Brownian loops centered in $D$ with le…