53 citations · 489 across the 66 of their papers we have counts for
9 papers · 1 filter
On the finiteness of the group associated with weighted walks in multidimensional orthants
Andrew Elvey Price, Emmanuel Humbert, Kilian Raschel
In the study of walks with small steps confined to multidimensional orthants, a certain group of transformations plays a central role. In particular, several techniques to potentia…
Persistence probabilities of MA(1) sequences with Laplace innovations and -deformed zigzag numbers
Frank Aurzada, Kilian Raschel
We study the persistence probabilities of a moving average process of order one with innovations that follow a Laplace distribution. The persistence probabilities can be computed f…
Asymptotics of returns to the coordinate axes for conditioned planar simple random walks
Rodolphe Garbit, Kilian Raschel
In this paper we study the number of returns to the coordinate axes for two-dimensional nearest-neighbour random walks. While one-dimensional results on returns are classical, much…
Boundary contacts for reflected random walks in the quarter plane
Viet Hung Hoang, Kilian Raschel
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lie…
Persistence probabilities for MA(1) sequences with uniform innovations
Frank Aurzada, Kilian Raschel
We study the persistence probabilities of a moving average process of order one with uniform innovations. We identify a number of regions-characterized by the location of the unifo…
Discrete harmonic polynomials in multidimensional orthants
Emmanuel Humbert, Kilian Raschel
We consider multidimensional random walks in pyramidal cones (or multidimensional orthants), which are intersections of a finite number of half-spaces. We explore the connection be…
Singular walks in the quarter plane and Bernoulli numbers
Alin Bostan, Lucia Di Vizio, Kilian Raschel
We consider singular (aka genus ) walks in the quarter plane and their associated generating functions , which enumerate the walks starting from the origin, of fixed e…
Limit shape of the leaky Abelian sandpile model with multiple layers
Théo Ballu, Cédric Boutillier, Sevak Mkrtchyan +1
In this paper we study a triple generalization of the Leaky Abelian Sandpile Model (LASM) of Alevy and Mkrtchyan, originally analyzed in the case of the square lattice in dimension…
Enumeration of walks in multidimensional orthants and reflection groups
Léa Gohier, Emmanuel Humbert, Kilian Raschel
We consider (random) walks in a multidimensional orthant. Using the idea of universality in probability theory, one can associate a unique polyhedral domain to any given walk model…