PhD student in probability
Laboratoire d'Analyse, Topologie et ProbabilitésEmail : mlaunaycmi.univmrs.fr
Office : R115
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.
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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 w_{k}, the probability of drawing a ball of a certain colour is proportional to w_{k} 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/w_{k} 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 w_{k} is nondecreasing. 

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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 1p) 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 w_{k} 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 w_{k}=ρ^{k}, 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. 
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Marches Aléatoires Renforcées (2008)Reinforced Random Walks


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Les théorèmes limites des processus de GaltonWatson (2006)Limit theorems for GaltonWatson processes

Last update : March 8, 2011