  A. We look at multidimensional random walks (Sn) n 0 in convex cones, and
address the question of whether two naturally associated generating functions
may define rational functions. The first series is the one of the survival
probabilities P($\tau$ > n), where $\tau$ is the first exit time from a given
cone; the second series is that of the excursion probabilities P($\tau$ > n, Sn
= y). Our motivation to consider this question is twofold: first, it goes along
with a global effort of the combinatorial community to classify the algebraic
nature of the series counting random walks in cones; second, rationality
questions of the generating functions are strongly associated with the
asymptotic behaviors of the above probabilities, which have their own interest.
Using wellknown relations between rationality of a series and possible
asymptotics of its coefficients, recent probabilistic estimates immediately
imply that the excursion generating function is not rational. Regarding the
survival probabilities generating function, we propose a short, elementary and
selfcontained proof that it cannot be rational neither.
