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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…
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…
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…
The extinction problem for a class of distylous plant populations
Gerold Alsmeyer, Kilian Raschel
In this paper, the extinction problem for a class of distylous plant populations is considered within the framework of certain nonhomogeneous nearest-neighbor random walks in the p…
Boundary behavior for random walks in cones
Kilian Raschel, Pierre Tarrago
We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem i…
Random Walks in the Quarter Plane Absorbed at the Boundary : Exact and Asymptotic
Kilian Raschel
Nearest neighbor random walks in the quarter plane that are absorbed when reaching the boundary are studied. The cases of positive and zero drift are considered. Absorption probabi…