10 papers · 1 filter
Asymptotics of returns to the coordinate hyperplanes for conditioned simple random walks
Rodolphe Garbit, Kilian Raschel
In this paper we study the number of returns to the coordinate hyperplanes for multidimensional nearest-neighbour random walks. While one-dimensional results on returns are classic…
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…
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 unif…
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…
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…