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An elementary approach to Gaussian multiplicative chaos

- N. Berestycki
- Mathematics
- 30 June 2015

A completely elementary and self-contained proof of convergence of Gaussian multiplicative chaos is given. The argument shows further that the limiting random measure is nontrivial in the entire… Expand

Recent progress in coalescent theory

- N. Berestycki
- PhysicsEnsaios Matemáticos
- 22 September 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… 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

Random walks on the random graph

- N. Berestycki, Eyal Lubetzky, Y. Peres, Allan Sly
- Mathematics, Computer Science
- 8 April 2015

TLDR

A phase transition in the random transposition random walk

- N. Berestycki, R. Durrett
- MathematicsDRW
- 16 March 2004

TLDR

Emergence of Giant Cycles and Slowdown Transition in Random Transpositions and k-Cycles

- N. Berestycki
- Mathematics
- 20 April 2010

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 phase transitions… 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

Random Hermitian matrices and Gaussian multiplicative chaos

- N. Berestycki, C. Webb, M. Wong
- Mathematics
- 12 January 2017

We prove that when suitably normalized, small enough powers of the absolute value of the characteristic polynomial of random Hermitian matrices, drawn from one-cut regular unitary invariant… 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

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