17 citations · 17 across the 5 of their papers we have counts for
5 papers
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…