53 citations · 489 across the 66 of their papers we have counts for
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Explicit expression for the generating function counting Gessel's walks
Irina Kurkova, Kilian Raschel
Gessel's walks are the planar walks that move within the positive quadrant by unit steps in any of the following directions: West, North-East, East and South-W…
Green functions for killed random walks in the Weyl chamber of Sp(4)
Kilian Raschel
We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of , which in addition satisfies the following property: for any ,…
Green functions and Martin compactification for killed random walks related to SU(3)
Kilian Raschel
We consider the random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior…
Passage time from four to two blocks of opinions in the voter model and walks in the quarter plane
Irina Kurkova, Kilian Raschel
A random walk in spatially homogeneous in the interior, absorbed at the axes, starting from an arbitrary point and with step probabilities drawn on Figure 1 is…
Random walks in with non-zero drift absorbed at the axes
Irina Kurkova, Kilian Raschel
Spatially homogeneous random walks in with non-zero jump probabilities at distance at most 1, with non-zero drift in the interior of the quadrant and absorbe…
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…