6 papers · 1 filter
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…
Weighted-amenability and percolation
Grigory Terlov, Ãdám Timár
In 1999, Benjamini, Lyons, Peres, and Schramm introduced a notion of weighted-amenability for transitive graphs that is equivalent to the amenability of its automorphism group. For…
Heavy repulsion of clusters in Bernoulli percolation
Sasha Bell, Tasmin Chu, Owen Rodgers +2
We study Bernoulli percolation on (non)unimodular quasi-transitive graphs and prove that, almost surely, for any two heavy clusters and , the set of vertices in wi…
Berry-Esseen Theorem for Sample Quantiles with Locally Dependent Data
Partha S. Dey, Grigory Terlov
We derive a Gaussian Central Limit Theorem for the sample quantiles based on locally dependent random variables with explicit convergence rate. Our approach is based on converting…