1 citations · 2 across the 8 of their papers we have counts for
13 papers
Elephants explore in spirals sometimes
Lucile Laulin, Bastien Mallein
We consider in this article an Elephant Random Walk evolving in the plane. Specifically, this is a reinforced stochastic process in which the th step is given by a random rotati…
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…
A universal scaling limit for diffusive amnesic step-reinforced random walks
Marco Bertenghi, Lucile Laulin
We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suita…
Elephant polynomials
Hélène Guérin, Lucile Laulin, Kilian Raschel
In this note, we study a family of polynomials that appear naturally when analysing the characteristic functions of the one-dimensional elephant random walk. These polynomials depe…
Recurrence of the plane Elephant random walk
Nicolas Curien, Lucile Laulin
We give a short proof of the recurrence of the two-dimensional elephant random walk in the diffusive regime. This was recently established by Shuo Qin, but our proof only uses very…
A fixed-point equation approach for the superdiffusive elephant random walk
Hélène Guérin, Lucile Laulin, Kilian Raschel
We study the elephant random walk in arbitrary dimension . Our main focus is the limiting random variable appearing in the superdiffusive regime. Building on a link betwee…
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…
How to estimate the memory of the Elephant Random Walk
Bernard Bercu, Lucile Laulin
We introduce an original way to estimate the memory parameter of the elephant random walk, a fascinating discrete time random walk on integers having a complete memory of its entir…
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…
On the multi-dimensional elephant random walk
Bernard Bercu, Lucile Laulin
The purpose of this paper is to investigate the asymptotic behavior of the multi-dimensional elephant random walk (MERW). It is a non-Markovian random walk which has a complete mem…