How much does a random walk wind around a given point? At the large scale this question has been well understood since the 80’s thanks to work by Spitzer, Belisle, Rudnick, Hu and many others. In 2017, Budd gave the first exact results for this problem, by solving it on the square lattice. In this talk I will describe my exact solutions for a more general class of models, namely walks with small steps.

Institut Denis Poisson, CNRS et Université de Tours