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Mickaël Launay

PhD student in probability

E-mail : mlaunaycmi.univ-mrs.fr
Office : R115

Welcome to my homepage !

I'm currently a Ph.D. student under the supervision of Vlada Limic in Marseille, France. I'm writing my thesis on interacting urn models.

My curriculum vitae

Reasearch

Preprints

PDF version Urns with simultaneous drawing (2011) Submitted in december 2011. Abstract.In classical urn models, one usually draws one ball with replacement at each time unit and then adds one ball of the same colour. Given a weight sequence wk, the probability of drawing a ball of a certain colour is proportional to wk where k is the number of balls of this colour. A classical result states that an urn fixates on one colour after a finite time if an only if the sum of all 1/wk is finite. In this paper we shall study the case when at each time unit we draw with replacement a number d>2 of balls and then add d new balls of matching colours. The main goal is to prove that the result in the case of unique drawing generalises assuming in addition that wk is non-decreasing.

PDF version      See on arΧiv Interacting Urn Models (2011) My first article ! Submitted. Abstract. The aim of this paper is to study the asymptotic behavior of strongly reinforced interacting urns with partial memory sharing. The reinforcement mechanism considered is as follows: draw at each step and for each urn a white or black ball from either all the urns combined (with probability p) or the urn alone (with probability 1-p) and add a new ball of the same color to this urn. The probability of drawing a ball of a certain color is proportional to wk where k is the number of balls of this color. The higher the p, the more memory is shared between the urns. The main results can be informally stated as follows: in the exponential case wk=ρk, if p≥1/2 then all the urns draw the same color after a finite time, and if p<1/2 then some urns fixate on a unique color and others keep drawing both black and white balls.

Theses

PDF version Marches Aléatoires Renforcées (2008) Reinforced Random Walks My master dissertation supervised by Vlada Limic. In french. Abstract. The aim of this thesis is to present differents results related to Sellke conjecture, which state that a strongly reinforced random walk on a graph G is almost surely attracted by a single edge. This work is mainly adapted form articles of Vlada Limic and Pierre Tarrès.

PDF version Les théorèmes limites des processus de Galton-Watson (2006) Limit theorems for Galton-Watson processes Magister disertation with Adrien Joseph and supervised by Jean-François Le Gall. In french Abstract. If (Zn)n is a Galton-Watson process with natality L satisfying E[L]=m>1 (supercritical case), we study the limit of Zn/mn that we denote by W. Surprisingly, the condition W=0 is not equivalent to the extinction of the process (Zn=0 after a finite time). The Kesten-Stigum theorem states that for natality laws such that E[Llog+(L)] is infinite, we have W=0 almost surely even on non extinction of the process. This thesis is based on chapter 11 of the book Probability on trees and networks by Russell Lyons and Yuval Peres.

Links

• MicMaths.com, un site que j'ai lancé en septembre 2008 et dans lequel j'essaye de proposer une approche originale et ludique des mathématiques.
• Un site un peu plus personnel
• Le séminaire des doctorants de Marseille
La page du CMI et celle du LATP
• L'école normale supérieure, le DMA

Last update : March 8, 2011