Title:

First-passage statistics  of non Markovian random walks and random search processes.

Abstract:

The first-passage time is a key quantity for evaluating the kinetics of various processes, and in particular chemical reactions involving “small” numbers of particles. A striking example is given by gene transcription, where specific proteins search for target sequences on DNA.

I will present asymptotic results which enable the determination of the  first-passage time statistics to a target site for a wide range of random processes  in  confined domains, and show how these results can be extended to non Markovian processes, including ageing processes, which are often needed to model transport in complex environments. I will discuss how these results can be used to assess the optimality of random search processes.