The Brownian loop measure on Riemann surfaces and applications to length
spectra
The Brownian loop measure on Riemann surfaces and applications to length
spectra
We prove a simple identity relating the length spectrum of a Riemann surface to that of the same surface with an arbitrary number of additional cusps. Our proof uses the Brownian loop measure introduced by Lawler and Werner. In particular, we express the total mass of Brownian loops in a …