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- Alin Bostan, Kilian Raschel, Bruno Salvy
- J. Comb. Theory, Ser. A
- 2014

We prove that the sequence (eSn )nâ‰¥0 of excursions in the quarter plane corresponding to a nonsingular step set S âŠ† {0, Â±1} with infinite group does not satisfy any nontrivial linear recurrence withâ€¦ (More)

Models of spatially homogeneous walks in the quarter plane Z2+ with steps taken from a subset S of the set of jumps to the eight nearest neighbors are considered. The generating function (x, y, z) 7â†’â€¦ (More)

Enumeration of planar lattice walks is a classical topic in combinatorics, at the cross-roads of several domains (e.g., probability, statistical physics, computer science). The aim of this paper isâ€¦ (More)

â€” Spatially homogeneous random walks in (Z+) with non-zero jump probabilities at distance at most 1, with non-zero drift in the interior of the quadrant and absorbed when reaching the axes areâ€¦ (More)

- Kilian Raschel
- 2011

We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of Sp(4), which in addition satisfies the following property: for any n > 3, there is in this family a walkâ€¦ (More)

- Pauline Lafitte-Godillon, Kilian Raschel, Viet-Chi Tran
- SIAM Journal of Applied Mathematics
- 2013

In this paper, we study a flower population in which self-reproduction is not permitted. Individuals are diploid, that is, each cell contains two sets of chromosomes, and distylous, that is, twoâ€¦ (More)

- Kilian Raschel
- 2010

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 probabilities at a givenâ€¦ (More)

- Rodolphe Garbit, Kilian Raschel
- 2013

We compute the exponential decay of the probability that a given multidimensional random walk stays in a convex cone up to time n, as n goes to infinity. We show that the latter equals the minimum,â€¦ (More)

- Kilian Raschel
- 2014

We propose a new approach for finding discrete harmonic functions in the quarter plane with Dirichlet conditions. It is based on solving functional equations that are satisfied by the generatingâ€¦ (More)

- Kilian Raschel
- 2010

The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to aâ€¦ (More)