Dresden 2026 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 7: Focus Session: Large Deviations and Rare Events I

DY 7.1: Hauptvortrag

Montag, 9. März 2026, 09:30–10:00, ZEU/0114

Fast Rare Events in Exit Times Distributions of Jump Processes — •Raffaella Burioni — Department of Mathematics, Physics and Computer Sciences, University of Parma, Italy — INFN - Sezione di Milano Bicocca - Parma, Italy

Rare events in first-passage and exit-time statistics of jump processes can play a decisive role in triggering anomalous reactions and extreme responses in a wide range of systems. This is particularly relevant when jump lengths or waiting times follow broad, heavy-tailed distributions, for which rare events are not exponentially suppressed and can significantly affect macroscopic observables. Interestingly, in the presence of heavy-tailed distributions, large fluctuations follow the Big Jump Principle, a counterintuitive mechanism according to which rare events arise not from the accumulation of many small deviations, but from a single, dominant fluctuation.

We present a general framework for estimating the contribution of fast rare events to exit probabilities in jump processes with fat-tailed distributions. We apply this approach to discrete-time random walks, Lévy walks, and the Lévy-Lorentz gas, which are widely used to describe transport in biological systems and disordered media. We derive the scaling form of the probability distribution for fast exit events, in which the process leaves a finite interval over distances much larger than the typical scale and on timescales orders of magnitude shorter than the characteristic timescale of the dynamics. We discuss extensions to N independent walkers, where collective effects can further enhance the contribution of fast rare events to exit statistics.

Keywords: Large deviations; Jumps processes; First passage Probability