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Branching random walks on binary search trees: convergence of the occupation measure

Eric Fekete (2010)

ESAIM: Probability and Statistics

We consider branching random walks with binary search trees as underlying trees. We show that the occupation measure of the branching random walk, up to some scaling factors, converges weakly to a deterministic measure. The limit depends on the stable law whose domain of attraction contains the law of the increments. The existence of such stable law is our fundamental hypothesis. As a consequence, using a one-to-one correspondence between binary trees and plane trees, we give a description of the...

Brownian particles with electrostatic repulsion on the circle : Dyson’s model for unitary random matrices revisited

Emmanuel Cépa, Dominique Lépingle (2001)

ESAIM: Probability and Statistics

The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices N × N is interpreted as a system of N interacting brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles N goes to infinity (through the empirical measure process). We prove that a limiting...

Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited

Emmanuel Cépa, Dominique Lépingle (2010)

ESAIM: Probability and Statistics

The Brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices N x N is interpreted as a system of N interacting Brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles N goes to infinity (through the empirical measure process). We prove...

Brownian penalisations related to excursion lengths, VII

B. Roynette, P. Vallois, M. Yor (2009)

Annales de l'I.H.P. Probabilités et statistiques

Limiting laws, as t→∞, for brownian motion penalised by the longest length of excursions up to t, or up to the last zero before t, or again, up to the first zero after t, are shown to exist, and are characterized.

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