20 citations · 75 across the 14 of their papers we have counts for
11 papers · 1 filter
The snake in the Brownian sphere
Omer Angel, Emmanuel Jacob, Brett Kolesnik +1
The Brownian sphere is a random metric space, homeomorphic to the two-dimensional sphere, which arises as the universal scaling limit of many types of random planar maps. The direc…
Annihilating branching Brownian motion
Daniel Ahlberg, Omer Angel, Brett Kolesnik
We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When oppos…
Large deviations of the greedy independent set algorithm on sparse random graphs
Brett Kolesnik
We study the greedy independent set algorithm on sparse Erdős-Rényi random graphs . This range of is of interest due to the threshold at , beyond whic…
Weakly saturated random graphs
Zsolt Bartha, Brett Kolesnik
As introduced by Bollobás, a graph is weakly -saturated if the complete graph is obtained by iteratively completing copies of minus an edge. For all graphs , we…
Transitive closure in a polluted environment
Janko Gravner, Brett Kolesnik
We introduce and study a new percolation model, inspired by recent works on jigsaw percolation, graph bootstrap percolation, and percolation in polluted environments. Start with an…
Randomized sequential importance sampling for estimating the number of perfect matchings in bipartite graphs
Persi Diaconis, Brett Kolesnik
We introduce and study randomized sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. In analyzing their performance, we e…
To stay discovered: On tournament mean score sequences and the Bradley--Terry model
David Aldous, Brett Kolesnik
On being told that a piece of work he thought was his discovery had duplicated an earlier mathematician's work, Larry Shepp once replied "Yes, but when {\em I} discovered it, it {\…
Sharp threshold for -percolation
Brett Kolesnik
We locate the critical threshold at which it becomes likely that the complete graph can be obtained from the Erdős-Rényi graph by iteratively completin…
Large deviations for subcritical bootstrap percolation on the random graph
Omer Angel, Brett Kolesnik
We study atypical behavior in bootstrap percolation on the Erdős-Rényi random graph. Initially a set is infected. Other vertices are infected once at least of their neighbo…
Thresholds for contagious sets in random graphs
Omer Angel, Brett Kolesnik
For fixed , we consider bootstrap percolation with threshold on the Erdős-Rényi graph . We identify a threshold for above which there is with high…
Stability of geodesics in the Brownian map
Omer Angel, Brett Kolesnik, Grégory Miermont
The Brownian map is a random geodesic metric space arising as the scaling limit of random planar maps. We strengthen the so-called confluence of geodesics phenomenon observed at th…