%0 Unpublished work
%T Conditions for some non stationary random walks in the quarter plane to be singular or of genus 0
%+ Symbolic Special Functions : Fast and Certified (SPECFUN)
%+ Robotics & Intelligent Transportation Systems (RITS)
%+ Saint Petersburg State Chemical Pharmaceutical University (SPCPA)
%A Fayolle, Guy
%A Iasnogorodski, Roudol
%8 2020-11-19
%D 2020
%Z Mathematics [math]/Probability [math.PR]Preprints, Working Papers, ...
%X We analyze the kernel K(x, y, t) of the basic functional equation associated with the tri-variate counting generating function (CGF) of walks in the quarter plane. In this short paper, taking $t ∈]0, 1[$, we provide the conditions on the step set {p i,j } to decide whether the walks are singular or regular, as defined in [3, Section 2.3]. These conditions are independent of $t ∈]0, 1[$ and given in terms of step set configurations. We also give the configurations for the kernel to be of genus 0, knowing that the genus is always ≤ 1. All these conditions are very similar to the case t = 1 considered in [3]. Our results extend the work [2], which considers only very special situations, namely when $t ∈]0, 1[$ is a transcendental number and the $p i,j s$ are rational.
%G English
%2 https://inria.hal.science/hal-03008556v2/document
%2 https://inria.hal.science/hal-03008556v2/file/noyau.pdf
%L hal-03008556
%U https://inria.hal.science/hal-03008556