Disconnection and non-intersection probabilities of Brownian motion on an annulus
Gefei Cai, Peking University
Abstract: We derive an exact formula for the probability that a Brownian path on an annulus does not disconnect the two boundary components of the annulus. The leading asymptotic behavior of this probability is governed by the disconnection exponent obtained by Lawler-Schramm-Werner (2001) using the connection to Schramm-Loewner evolution (SLE). The derivation of our formula is based on this connection and the coupling with Liouville quantum gravity (LQG), from which we can exactly compute the conformal moduli of random annular domains defined by SLE curves. Using a similar approach, we also derive exact formulas for the non-intersection probabilities of independent Brownian paths on an annulus, as well as extend the result to the case of Brownian loop soup. Based on joint work with X. Fu, X. Sun, and Z. Xie, and upcoming work with Z. Xie.
