Section: New Results

Martin boundary of killed random walks on isoradial graphs

Alin Bostan contributed to an article by Cédric Boutillier and Kilian Raschel [15], devoted to the study of random walks on isoradial graphs. Contrary to the lattice case, isoradial graphs are not translation invariant, do not admit any group structure and are spatially non-homogeneous. However, Boutillier and Raschel have been able to obtain analogues of a celebrated result by Ney and Spitzer (1966) on the so-called Martin kernel (ratio of Green functions started at different points). Alin Bostan provided in the Appendix two different proofs of the fact that some algebraic power series arising in this context have non-negative coefficients.