Statistics of two-dimensional random walks, the "cyclic sieving phenomenon" and the Hofstadter model

Stefan Mashkevich, Stéphane Ouvry, Alexios Polychronakos

We focus on the algebraic area probability distribution of planar random walks on a square lattice with $m_1$, $m_2$, $l_1$ and $l_2$ steps right, left, up and down. We aim, in par…