53 citations · 489 across the 66 of their papers we have counts for
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On the first hitting time of a high-dimensional orthant
Emmanuel Humbert, Kilian Raschel
We consider a collection of independent standard Brownian particles (or random walks), starting from a configuration where at least one particle is positive, and study the first ti…
Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness
Thomas Dreyfus, Andrew Elvey Price, Kilian Raschel
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in…
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…
Invariant measure of gaps in degenerate competing three-particle systems
Sandro Franceschi, Tomoyuki Ichiba, Ioannis Karatzas +1
We study the gap processes in a degenerate system of three particles interacting through their ranks. We obtain the Laplace transform of the invariant measure of these gaps, and an…
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…