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....
In recent times, several rigorous results on simple random exchange models were proved. In this talk, after a short review of the literature, I focus on a subset of results in a recent paper in which we discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this model and, under...
Deviations from the standard laws of Brownian motion, the linear time dependence
of the mean squared displacement and the Gaussian probability density function,
are quite commonly observed in an adundance of systems. The physical mechanisms
for these anomalies are non-universal, prompting the need for different stochastic
models along with their identification from measured time series of...
