5 papers
On the direct SLE-martingale approach to the integrability of Conformal Loop Ensembles
Jason Miller, Wendelin Werner
This paper is about the derivation of "integrability results" (i.e., for example, explicit formulas for the probability of events involving a few marked points) for Conformal Loop…
Intensity doubling for Brownian loop-soups in high dimensions
Titus Lupu, Wendelin Werner
We derive an intensity doubling feature of critical Brownian loop-soups on the cable-graphs of for that can be described as follows: In the box $[-N, N]^d…
On Loops in critical high-dimensional percolation
Amelia Carpenter, Wendelin Werner
We show the following results about critical Bernoulli percolation in high dimensions: In a box of side-length N, there exist self-avoiding open loops of diameter comparable to N,…
A switching identity for cable-graph loop soups and Gaussian free fields
Wendelin Werner
We derive a "switching identity" that can be stated for critical Brownian loop-soups or for the Gaussian free field on a cable graph: It basically says that at the level of cluster…
Parity questions in critical planar Brownian loop-soups (or "where did the free planar bosons go?")
Matthis Lehmkuehler, Wei Qian, Wendelin Werner
The critical two-dimensional Brownian loop-soup is an infinite collection of non-interacting Brownian loops in a planar domain that possesses some combinatorial features related to…