Global divergence of spatial coalescents (2009)
Angel, Omer, Berestycki, Nathanael, Limic, Vlada
A class of processes called spatial \Lambda-coalescents was recently introduced by Limic and Sturm (2006). In these models particles perform independent random walks on some underlying graph G. In...
Recent progress in coalescent theory (2009)
Coalescent theory is the study of random processes where particles may join each other to form clusters as time evolves. These notes provide an introduction to some aspects of the mathematics of...
The $\Lambda$-coalescent speed of coming down from infinity (2008)
Berestycki, Julien, Berestycki, Nathanael, Limic, Vlada
Consider a $\Lambda$-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number $N_t$ of blocks at...
A double phase transition arising from Brownian entropic repulsion (2008)
Benjamini, Itai, Berestycki, Nathanael
We analyze one-dimensional Brownian motion conditioned on a self-repelling behaviour. In the main result of this paper, it is shown that a double phase transition occurs when the growth of the local...
Brownian Entropic Repulsion (2008)
Benjamini, Itai, Berestycki, Nathanael
We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a...
Limiting behavior for the distance of a random walk (2008)
Berestycki, Nathanael; University Of Cambridge; N.Berestycki@statslab.cam.ac.uk, Durrett, Rick; Cornell University; Rtd1@cornell.edu
In this paper we study some aspects of the behavior of random walks on large but finite graphs before they have reached their equilibrium distribution. This investigation is motivated by a result we...
Gibbs distributions for random partitions generated by a fragmentation process (2005)
Berestycki, Nathanael, Pitman, Jim
In this paper we study random partitions of 1,...n, where every cluster of size j can be in any of w_j possible internal states. The Gibbs (n,k,w) distribution is obtained by sampling uniformly among...
Gibbs distributions for random partitions generated by a fragmentation process (2005)
Berestycki, Nathanael, Pitman, Jim
In this paper we study random partitions of 1,...n, where every cluster of size j can be in any of w_j possible internal states. The Gibbs (n,k,w) distribution is obtained by sampling uniformly among...
A phase transition in the random transposition random walk (2004)
Berestycki, Nathanael, Durrett, Rick
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 result about the random...
A phase transition in the random transposition random walk (2004)
Berestycki, Nathanael, Durrett, Rick
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 result about the random...