10 citations · 10 across the 13 of their papers we have counts for
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On the finiteness of the group associated with weighted walks in multidimensional orthants
Andrew Elvey Price, Emmanuel Humbert, Kilian Raschel
In the study of walks with small steps confined to multidimensional orthants, a certain group of transformations plays a central role. In particular, several techniques to potentia…
Singular walks in the quarter plane and Bernoulli numbers
Alin Bostan, Lucia Di Vizio, Kilian Raschel
We consider singular (aka genus ) walks in the quarter plane and their associated generating functions , which enumerate the walks starting from the origin, of fixed e…
Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness
Thomas Dreyfus, Andrew Elvey Price, Kilian Raschel
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in…
Elephant polynomials
Hélène Guérin, Lucile Laulin, Kilian Raschel
In this note, we study a family of polynomials that appear naturally when analysing the characteristic functions of the one-dimensional elephant random walk. These polynomials depe…
Logarithmic terms in discrete heat kernel expansions in the quadrant
Andrew Elvey-Price, Andreas Nessmann, Kilian Raschel
In the context of lattice walk enumeration in cones, we consider the number of walks in the quarter plane with fixed starting and ending points, prescribed step-set and given lengt…
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…