Generalized disconnection exponents for Brownian loop-soups
We study the question of whether there exist double points on the boundaries of clusters in Brownian loop-soups — an object introduced by Lawler and Werner in 2004. This question is closely related to our earlier works (with Werner) on the decomposition of Brownian loop-soup clusters. More concretely, we introduce a notion of disconnection exponents which generalizes the Brownian disconnection exponents derived by Lawler, Schramm and Werner in 2001. By computing the generalized disconnection exponents, we can predict the dimension of multiple points on the cluster boundaries in loop-soups. However, for the critical intensity of loop-soup, the dimension of double points on the cluster boundaries appears to be zero, leaving the open problem of whether such points exist for the critical loop-soup.
Date: 24 June 2019, 14:00 (Monday, 9th week, Trinity 2019)
Venue: Mathematical Institute, Woodstock Road OX2 6GG
Venue Details: L4
Speaker: Wei Qian (University of Cambridge)
Organising department: Department of Statistics
Part of: Probability seminar
Booking required?: Not required
Audience: Public
Editor: Christina Goldschmidt