10 papers
Interface between competing random walks on a cycle
Shirshendu Chatterjee, Nadya Nabahi, Grigory Terlov
We consider a competition between two independent random walks on a cycle of length . Each vertex is claimed by the walker that visits it first, and remains claimed thereafter.…
Random optimization problems at fixed temperatures
Partha S. Dey, Grigory Terlov
This article considers a class of disordered mean-field combinatorial optimization problems. We focus on the Gibbs measure, where the inverse temperature does not vary with the siz…
Limiting distributions of triangle counts in linear preferential attachment models
Partha S. Dey, Grigory Terlov
We derive distributional approximations for the number of triangles in the linear preferential attachment model , where and , with explicit rate…
Whitney's 2-isomorphism theorem for graphings
Márton Borbényi, Grigory Terlov, László Márton Tóth
We prove measurable analogues of Whitney's classical theorems on weak isomorphisms of finite graphs. In the setting of locally finite graphings, we introduce a notion of weak isomo…
Nonamenable subforests of multi-ended quasi-pmp graphs
Ruiyuan Chen, Grigory Terlov, Anush Tserunyan
We prove the a.e. nonamenability of locally finite quasi-pmp Borel graphs whose every component admits at least three nonvanishing ends with respect to the underlying Radon--Nikody…
Measurable one-ended spanning trees
Matt Bowen, António Girão, Héctor Jardón-Sánchez +1
We show that a one-ended, locally finite, measurable graph on a standard probability space admits a measurable one-ended spanning subtree if and only if it is measure-hyperfinite.…