5 citations · 10 across the 5 of their papers we have counts for
5 papers
Quadrant Walks Starting Outside the Quadrant
Manfred Buchacher, Manuel Kauers, Amelie Trotignon
We investigate a functional equation which resembles the functional equation for the generating function of a lattice walk model for the quarter plane. The interesting feature of t…
On the nature of four models of symmetric walks avoiding a quadrant
Thomas Dreyfus, Amélie Trotignon
We study the nature of the generating series of some models of walks with small steps in the three quarter plane. More precisely, we restrict ourselves to the situation where the g…
Discrete harmonic functions in the three-quarter plane
Amélie Trotignon
In this article we are interested in finding positive discrete harmonic functions with Dirichlet conditions in three quadrants. Whereas planar lattice (random) walks in the quadran…
On walks avoiding a quadrant
Kilian Raschel, Amélie Trotignon
Two-dimensional (random) walks in cones are very natural both in combinatorics and probability theory: they are interesting for themselves and also because they are strongly relate…
3d positive lattice walks and spherical triangles
B Bogosel, V Perrollaz, K. Raschel +1
In this paper we explore the asymptotic enumeration of three-dimensional excursions confined to the positive octant. As shown in [29], both the exponential growth and the critical…