I will discuss the analytic method for counting walks with small steps in the quarter plane, which has been heavily used in the classification of these walk models. In particular I will describe how it can be extended to walks in the 3/4-plane. In particular this work proves a conjecture of Dreyfus and Trotignon that the complexity (algebraic, D-finite, D-algebraic, etc.) of the generating function Q(x,y;t) counting walks in the quarter plane is the same as that of the generating function C(x,y;t) counting walks in the three-quarter plane, at least with respect to the variables x and y.
LaBRI salle 76 (+ visioconférence zoom)