53 citations · 489 across the 66 of their papers we have counts for
4 papers · 1 filter
On the functions counting walks with small steps in the quarter plane
Irina Kurkova, Kilian Raschel
Models of spatially homogeneous walks in the quarter plane with steps taken from a subset of the set of jumps to the eight nearest neighbors are consi…
Random walks reaching against all odds the other side of the quarter plane
Johan S. H. van Leeuwaarden, Kilian Raschel
For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state , we study the event that the walk reaches the vertical ax…
Random walks in the quarter plane with zero drift: an explicit criterion for the finiteness of the associated group
Guy Fayolle, Kilian Raschel
In many recent studies on random walks with small jumps in the quarter plane, it has been noticed that the so-called "group" of the walk governs the behavior of a number of quantit…
The compensation approach for walks with small steps in the quarter plane
Ivo J. B. F. Adan, Johan S. H. van Leeuwaarden, Kilian Raschel
This paper is the first application of the compensation approach to counting problems. We discuss how this method can be applied to a general class of walks in the quarter plane $Z…