17 citations · 17 across the 5 of their papers we have counts for
6 papers · 1 filter
Two Phase Transitions for the Contact Process on Small Worlds
Rick Durrett, Paul Jung
In our version of Watts and Strogatz's small world model, space is a d-dimensional torus in which each individual has in addition exactly one long-range neighbor chosen at random f…
A coalescent model for the effect of advantageous mutations on the genealogy of a population
Rick Durrett, Jason Schweinsberg
When an advantageous mutation occurs in a population, the favorable allele may spread to the entire population in a short time, an event known as a selective sweep. As a result, wh…
Random partitions approximating the coalescence of lineages during a selective sweep
Jason Schweinsberg, Rick Durrett
When a beneficial mutation occurs in a population, the new, favored allele may spread to the entire population. This process is known as a selective sweep. Suppose we sample in…
Random Oxford Graphs
Jonah Blasiak, Rick Durrett
Inspired by a concept in comparative genomics, we investigate properties of randomly chosen members of G_1(m,n,t), the set of bipartite graphs with left vertices, n right verti…
Power laws for family sizes in a duplication model
Rick Durrett, Jason Schweinsberg
Qian, Luscombe and Gerstein [J. Molecular Biol. 313 (2001) 673--681] introduced a model of the diversification of protein folds in a genome that we may formulate as follows. Consid…
A phase transition in the random transposition random walk
Nathanael Berestycki, Rick Durrett
Our work is motivated by Bourque and Pevzner's (2002) simulation study of the effectiveness of the parsimony method in studying genome rearrangement, and leads to a surprising resu…