53 citations · 489 across the 66 of their papers we have counts for
6 papers · 1 filter
Lattice walks confined to an octant in dimension 3: (non-)rationality of the second critical exponent
Luc Hillairet, Helen Jenne, Kilian Raschel
In the field of enumeration of walks in cones, it is known how to compute asymptotically the number of excursions (finite paths in the cone with fixed length, starting and ending p…
Asymptotics of arithmetic functions of GCD and LCM of random integers in hyperbolic regions
Alexander Iksanov, Alexander Marynych, Kilian Raschel
We prove limit theorems for the greatest common divisor and the least common multiple of random integers. While the case of integers uniformly distributed on a hypercube with growi…
Persistence for a class of order-one autoregressive processes and Mallows-Riordan polynomials
Gerold Alsmeyer, Alin Bostan, Kilian Raschel +1
We establish exact formulae for the persistence probabilities of an AR(1) sequence with symmetric uniform innovations in terms of certain families of polynomials, most notably a fa…
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 stationary distribution of reflected Brownian motion in a non-convex wedge
Guy Fayolle, Sandro Franceschi, Kilian Raschel
We study the stationary reflected Brownian motion in a non-convex wedge, which, compared to its convex analogue model, has been much rarely analyzed in the probabilistic literature…
On the stationary distribution of reflected Brownian motion in a wedge: differential properties
M. Bousquet-Mélou, A. Elvey Price, S. Franceschi +2
We consider the classical problem of determining the stationary distribution of the semimartingale reflected Brownian motion (SRBM) in a two-dimensional wedge. Under standard assum…