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Quantifying memory effects in random search processes
A general question that arises in random walk theory is the quantification of space exploration by a random walker. A key observable is provided by the first-passage time, which quantifies the kinetics of general target search problems, and as such has a broad range of applications from diffusion limited reactions at the molecular scale, to immune cells patrolling tissues to find antigens, or larger scale organisms looking for ressources.
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, and show how these results generalize to non Markovian processes, which are needed to model non Brownian, complex searchers with memory skills. An explicit example of cellular system where long range memory effects emerge will be given.