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Parking on the Random Recursive Tree
Alice Contat, Lucile Laulin
We study the parking process on the random recursive tree. We first prove that although the random recursive tree has a non-degenerate Benjamini--Schramm limit, the phase transitio…
On the limit law of the superdiffusive elephant random walk
Hélène Guérin, Lucile Laulin, Kilian Raschel +1
When the memory parameter of the elephant random walk is above a critical threshold, the process becomes superdiffusive and, once suitably normalised, converges to a non-Gaussian r…
Introducing smooth amnesia to the memory of the Elephant Random Walk
Lucile Laulin
This paper is devoted to the asymptotic analysis of the amnesic elephant random walk (AERW) using a martingale approach. More precisely, our analysis relies on asymptotic results f…
New insights on the reinforced Elephant Random Walk using a martingale approach
Lucile Laulin
This paper is devoted to the asymptotic analysis of the reinforced elephant random walk (RERW) using a martingale approach. In the diffusive and critical regimes, we establish the…
A martingale approach for Pólya urn processes
Lucile Laulin
This paper is devoted to a direct martingale approach for P{ó}lya urn models asymptotic behaviour. A P{ó}lya process is said to be small when the ratio of its remplacement matrix e…
On the center of mass of the elephant random walk
Bernard Bercu, Lucile Laulin
Our goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discrete-time random walk on integers with a complete memory of its…