44 citations · 120 across the 13 of their papers we have counts for
13 papers
A human proof of Gessel's lattice path conjecture
Alin Bostan, Irina Kurkova, Kilian Raschel
Gessel walks are lattice paths confined to the quarter plane that start at the origin and consist of unit steps going either West, East, South-West or North-East. In 2001, Ira Gess…
New steps in walks with small steps in the quarter plane
Irina Kurkova, Kilian Raschel
In this article we obtain new expressions for the generating functions counting (non-singular) walks with small steps in the quarter plane. Those are given in terms of infinite ser…
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…
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…
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…