15 citations · 29 across the 9 of their papers we have counts for
10 papers
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…
A family of Fourier transform's eigenfunctions
Rodolphe Garbit, Julien-Bilal Zinoune
This paper presents a family of Fourier eigenfunctions indexed by the space dimension d. These eigenfunctions are radial and built upon some generalized exponential integral functi…
Random walks with drift inside a pyramid: convergence rate for the survival probability
Rodolphe Garbit, Kilian Raschel
We consider multidimensional random walks in pyramids, which by definition are cones formed by finite intersections of half-spaces. The main object of interest is the survival prob…
The generating function of the survival probabilities in a cone is not rational
Rodolphe Garbit, Kilian Raschel
A. We look at multidimensional random walks (Sn) n 0 in convex cones, and address the question of whether two naturally associated generating functions may define rational function…
On the exit time from an orthant for badly oriented random walks
Rodolphe Garbit
In a recent paper, K. Raschel and R. Garbit proved that the exponential decreasing rate of the probability that a random walk (with all exponential moments) stays in a -dimensio…
On the exit time from a cone for Brownian motion with drift
Rodolphe Garbit, Kilian Raschel
We investigate the tail distribution of the first exit time of Brownian motion with drift from a cone and find its exact asymptotics for a large class of cones. Our results show in…