10 citations · 10 across the 1 of their papers we have counts for
10 papers
Martin boundary of random walks in convex cones
Jetlir Duraj, Kilian Raschel, Pierre Tarrago +1
We determine the asymptotic behavior of the Green function for zero-drift random walks confined to multidimensional convex cones. As a consequence, we prove that there is a unique…
Polyharmonic functions and random processes in cones
Francois Chapon, Eric Fusy, Kilian Raschel
We investigate polyharmonic functions associated to Brownian motion and random walks in cones. These are functions which cancel some power of the usual Laplacian in the continuous…
Martin boundary of killed random walks on isoradial graphs
Cédric Boutillier, Kilian Raschel
We consider killed planar random walks on isoradial graphs. Contrary to the lattice case, isoradial graphs are not translation invariant, do not admit any group structure and are s…
Plane bipolar orientations and quadrant walks
Mireille Bousquet-Mélou, Éric Fusy, Kilian Raschel
Bipolar orientations of planar maps have recently attracted some interest in combinatorics, probability theory and theoretical physics. Plane bipolar orientations with edges ar…
On the least common multiple of several random integers
Alin Bostan, Alexander Marynych, Kilian Raschel
Let denote the least common multiple of independent random integers uniformly chosen in . In this note, using a purely probabilistic approach, we de…
On walks avoiding a quadrant
Kilian Raschel, Amélie Trotignon
Two-dimensional (random) walks in cones are very natural both in combinatorics and probability theory: they are interesting for themselves and also because they are strongly relate…