On some properties of classical and quantum random walks.Санкт-Петербург

This talk is devoted to homogeneous random walks on a line. In the classical case, the generating function for the positive half-line ашrst passage time is discussed. It often turns out to admit an algebraic equation and is useful in statistical computations. Besides, the corresponding algebraic curve sometimes is rational and has a positive genus which can be accounted via analyzing singularities. An open quantum system $\rho \mapsto \sum_i V_i\rho V_i^*$ where $V_i$ are operators of shift on $a_i$ with coeffcients $\sqrt{p_i}$ is similar to the classical random walk with increases $a_i$ and their probabilities $p_i$. Some characteristics of it are computed.