Seminario di Matematica del Dottorato

Is the process by which particles spread out from a concentrated area to a less concentrated area. Given some regularity assumptions, classical diffusion is obtained thanks to the Central Limit Theorem and invariance principles. A signature of Classical diffusion is the mean square displacement that scales linearly. However, upon closer examination, many diffusion processes  with self-interaction or interaction with the medium present different scaling of the mean square displacement. This phenomenon is known as anomalous diffusion. In this talk we are going to consider a flexible model for anomalous diffusion on the plane. This model relies on polynomial space-time drifts as the mechanism that drives the anomalous diffusion. This model was motivated by an heuristic connection to a self-interacting, planar random walk which interacts with its own centre of mass via an excluded-volume mechanism,  and is conjectured to be superdiffusive with a scale exponent 3/4.  The main goal of the talk is to explain this heuristic connection.
The talk is based on a joint work with Mikhail Menshikov, Vadim Shcherbakov, and Andrew Wade, for details see https://arxiv.org/abs/2307.07458