BROWNIAN NON-MARKOVIAN EFFECTS IN TARGETING PROBLEMS

The aim of this thesis is the study of the statistics of targeting and first-passage problems for a class of Brownian yet non Gaussian stochastic processes. In particular to focus on the extreme first passage time where, unlike the commonly used mean first passage time, one is interested in the time it takes for the fastest among many searchers to find a target, a problem that is central in diffusion-limited reactions and biological processes such as human fertilization. This study, that will be mainly analytical and based on the theory of extreme values, will be applied to models such as diffusing diffusivity and polymers in the grand-canonical ensemble that are known to display non-Gaussian diffusion at early times.