How long does it take a random walker to reach a given target? This quantity, known as a first-passage time (FPT), has been the subject of a growing number of theoretical studies over the past decade. The importance of FPTs originates from the crucial role played by properties related to first encounters in various real situations, including transport in disordered media, diffusion limited reactions, or more generally target search processes. First-passage times in confinement, their optimization and their relationship to biophysical experiments are at the heart of this project. The following two issues will be investigated.
1) We will determine key first-passage observables of general scale-invariant random walks in confinement, which up to now have remained inaccessible: FPT distribution in the presence of several targets and/or several searchers, statistical properties of the explored territory, FPT distribution of a non-Markovian random walker. Beyond their theoretical interest, these developments will allow us to address in close connection with single-molecule experiments the importance of transport and spatial organization for gene transcription kinetics and stochastic gene expression.
2) We will address the question of the optimization of the search time. We have recently introduced a new type of search strategies, the intermittent strategies, which minimize the search time under general conditions. Here, the objectives are: (i) to determine new first-passage observables of these intermittent processes (eg the full FPT distribution) to allow the comparison of optimal strategies to experimental situations; (ii) to understand the physical mechanisms underlying real intermittent pathways and assess their optimality at the molecular (homologous recombination kinetics), cellular (search for infection markers by dendritic cells) and macroscopic scales (individual search behavior of ants); (iii) to use intermittent strategies to design efficient searches.
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