53 citations · 489 across the 66 of their papers we have counts for
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math.CO2017★ 7 cited
Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks
Thomas Dreyfus, Kilian Raschel
We consider weighted small step walks in the positive quadrant, and provide algebraicity and differential transcendence results for the underlying generating functions: we prove th…
math.CO2017★ 51 cited
Counting quadrant walks via Tutte's invariant method
Olivier Bernardi, Mireille Bousquet-Mélou, Kilian Raschel
In the 1970s, William Tutte developed a clever algebraic approach, based on certain "invariants", to solve a functional equation that arises in the enumeration of properly colored…
math.PR2017★ 15 cited
Integral expression for the stationary distribution of reflected brownian motion in a wedge
Sandro Franceschi, Kilian Raschel
For Brownian motion in a (two-dimensional) wedge with negative drift and oblique reflection on the axes, we derive an explicit formula for the Laplace transform of its stationary d…