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 …

Enumeration of three-quadrant walks via invariants: some diagonally symmetric models Page 1
Canad. J. Math. 2022, pp. 1–67 http://dx.doi.org/10.4153/S0008414X22000487 © The …

In this work we consider two different aspects of weighted walks in cones. To begin we
examine a particular weighted model, known as the Gouyou-Beauchamps model. Using the …

While discrete harmonic functions have been objects of interest for quite some time, this is
not the case for discrete polyharmonic functions, as appear for instance in the asymptotics of …

In this paper, we study the positive solutions to a discrete harmonic function for a random
walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded …

We determine the asymptotic behavior of the Green function for zero-drift random walks
confined to multidimensional convex cones. As a consequence, we prove that there is a …

We propose a systematic construction of signed harmonic functions for discrete Laplacian
operators with Dirichlet conditions in the quarter plane. In particular, we prove that the set of …

We prove that for recurrent, reversible graphs, the following conditions are equivalent:(a)
existence and uniqueness of the potential kernel,(b) existence and uniqueness of harmonic …

The field of analytic combinatorics, which studies the asymptotic behaviour of sequences
through analytic properties of their generating functions, has led to the development of deep …

We investigate harmonic functions and the convergence of the sequence of ratios (P _x (τ _
ϑ> n)/P _e (τ _ ϑ> n))(P x (τ ϑ> n)/P e (τ ϑ> n)) for a random walk on a countable group …