53 citations · 489 across the 66 of their papers we have counts for
5 papers · 1 filter
Differential transcendence of Bell numbers and relatives: a Galois theoretic approach
Alin Bostan, Lucia Di Vizio, Kilian Raschel
In 2003 Klazar proved that the ordinary generating function of the sequence of Bell numbers is differentially transcendental over the field of meromorphic funct…
Constructing discrete harmonic functions in wedges
Viet Hung Hoang, Kilian Raschel, Pierre Tarrago
We propose a systematic construction of signed harmonic functions for discrete Laplacian operators with Dirichlet conditions in the quarter plane. In particular, we prove that the…
Reflected random walks and unstable Martin boundary
Irina Ignatiouk-Robert, Irina Kourkova, Kilian Raschel
We introduce a family of two-dimensional reflected random walks in the positive quadrant and study their Martin boundary. While the minimal boundary is systematically equal to a un…
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…