Center Poncelet and LPTMS, CNRS
Large deviations in statistics of a two-dimensional random walk with forbidden voids
We discuss two examples of systems in which imposed external constraints push the underlying stochastic process in the "improbable regime" possessing the anomalous statistics. The first example deals with a two-dimensional biased random walk along a channel with some "contractions" (excluded voids of different shapes). We are interested in a typical span of a random walks above the tip of the void. The second example deals with the fluctuations of a two-dimensional random walk above a circle in a special regime of "elongated" trajectories. We propose the simple scaling consideration justified by the conformal approach for the second model.