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Branching Brownian motion seen from its tip

- E. Aïdékon, J. Berestycki, E. Brunet, Z. Shi
- Mathematics
- 19 April 2011

It has been conjectured since the work of Lalley and Sellke (Ann. Probab., 15, 1052–1061, 1987) that branching Brownian motion seen from its tip (e.g. from its rightmost particle) converges to an… Expand

Exchangeable Fragmentation-Coalescence Processes and their Equilibrium Measures

- J. Berestycki
- Mathematics, Economics
- 9 March 2004

We define and study a family of Markov processes with state space the compact set of all partitions of $N$ that we call exchangeable fragmentation-coalescence processes. They can be viewed as a… Expand

Small-time behavior of beta coalescents

- J. Berestycki, N. Berestycki, Jason Schweinsberg
- Mathematics
- 2 January 2006

For a finite measureon (0,1), the �-coalescent is a coalescent process such that, whenever there are b clusters, each k-tuple of clusters merges into one at rate R 1 0 x k 2 (1 x) b k �(dx). It has… Expand

BETA-COALESCENTS AND CONTINUOUS STABLE RANDOM TREES

- J. Berestycki, N. Berestycki, Jason Schweinsberg
- Mathematics
- 7 February 2006

TLDR

Ranked Fragmentations

- J. Berestycki
- Mathematics
- 25 April 2006

. In this paper we deﬁne and study self-similar ranked fragmentations. We ﬁrst show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a… Expand

The genealogy of branching Brownian motion with absorption

- J. Berestycki, N. Berestycki, Jason Schweinsberg
- Mathematics
- 13 January 2010

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 population stays roughly… Expand

The Λ-coalescent speed of coming down from infinity

- J. Berestycki, N. Berestycki, V. Limic
- Mathematics
- 27 July 2008

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… Expand

The number of accessible paths in the hypercube

- J. Berestycki, 'Eric Brunet, Z. Shi
- Mathematics, Computer Science
- 31 March 2013

TLDR

Multifractal Spectra of Fragmentation Processes

- J. Berestycki
- Mathematics
- 1 November 2003

AbstractLet (S(t),t≥0) be a homogeneous fragmentation of ]0,1[ with no loss of mass. For x∈]0,1[, we say that the fragmentation speed of x is v if and only if, as time passes, the size of the… Expand

The prolific backbone for supercritical superdiffusions

- J. Berestycki, A. Kyprianou, Antonio Murillo
- Mathematics
- 23 December 2009

We develop an idea of Evans and O'Connell, Englander and Pinsky and Duquesne and Winkel by giving a pathwise construction of the so called `backbone' decomposition for supercritical superprocesses.… Expand

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