7 papers · 1 filter
The Brownian loop-catcher
Gefei Cai
We introduce a family of random connected closed subsets of planar Brownian motion, called Brownian loop-catchers, which interpolate between the continuum loop-erased random-walk (…
Boundary four-point connectivities of conformal loop ensembles
Gefei Cai
We derive the boundary four-point Green's functions for conformal loop ensembles (CLE) with . Specializing to and , we establish the exact formulas for…
Uniqueness of generalized conformal restriction measures and Malliavin-Kontsevich-Suhov measures for
Gefei Cai, Yifan Gao
In this paper, we present a unified approach to establish the uniqueness of generalized conformal restriction measures with central charge in both chordal and radial…
Backbone probability of planar Brownian motion
Gefei Cai, Zhuoyan Xie
Motivated by critical planar percolation, we investigate a ``backbone'' event of planar Brownian motion, i.e.~the existence of two disjoint subpaths on the Brownian trajectory conn…
Three-point connectivity constant for -state Potts spin clusters
Gefei Cai, Haoyu Liu, Baojun Wu +1
Recently, Ang--Cai--Sun--Wu (2024) determined the three-point connectivity constant for two-dimensional critical percolation, confirming a prediction of Delfino and Viti (2010). In…
Disconnection probability of Brownian motion on an annulus
Gefei Cai, Xuesong Fu, Xin Sun +1
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…