4 papers · 1 filter
Coupling Brownian loop soups and random walk loop soups at all polynomial scales
Wei Qian
Lawler and Trujillo Ferreras constructed a well-known coupling between the Brownian loop soups on and the (discrete-time) random walk loop soups on (o…
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…
Multiple points on the boundaries of Brownian loop-soup clusters
Yifan Gao, Xinyi Li, Wei Qian
For a Brownian loop soup with intensity in the unit disk, we show that almost surely, the set of simple (resp. double) points on any portion of boundary of any of its c…
Conformal invariance of double random currents I: identification of the limit
Hugo Duminil-Copin, Marcin Lis, Wei Qian
This is the first of two papers devoted to the proof of conformal invariance of the critical double random current model on the square lattice. More precisely, we show the converge…