107 citations · 586 across the 55 of their papers we have counts for
5 papers · 1 filter
Survival of near-critical branching Brownian motion
Julien Berestycki, Nathanaël Berestycki, Jason Schweinsberg
Consider a system of particles performing branching Brownian motion with negative drift and killed upon hitting zero. Initially there is one particle at . Ke…
A conditioning principle for Galton-Watson trees
Nathanael Berestycki, Peter Morters, Nadia Sidorova
We show that an infinite Galton-Watson tree, conditioned on its martingale limit being smaller than $\eps$, converges as $\eps\downarrow 0$ in law to the regular -ary tree, wher…
Emergence of giant cycles and slowdown transition in random transpositions and -cycles
Nathanael Berestycki
Consider the random walk on the permutation group obtained when the step distribution is uniform on a given conjugacy class. It is shown that there is a critical time at which two…
The genealogy of branching Brownian motion with absorption
Julien Berestycki, Nathanaël Berestycki, Jason Schweinsberg
We consider a system of particles which perform branching Brownian motion with negative drift and are killed upon reaching zero, in the near-critical regime where the total populat…
Mixing times for random k-cycles and coalescence-fragmentation chains
Nathanaël Berestycki, Oded Schramm, Ofer Zeitouni
Let be the permutation group on elements, and consider a random walk on whose step distribution is uniform on -cycles. We prove a well-known…