5 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…
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…
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 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…