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math.PR2026
A quadratic ancestor inequality for spanning trees
Gefei Cai
We introduce a quadratic ancestor inequality for weighted spanning trees on finite undirected graphs and give two applications. First, for every finite -vertex transitive graph,…
math.PR2026
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 (…
math.PR2026
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 the…