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In noisy environments such as the cell, many processes involve target sites that are often hidden or inactive, and thus not always available for reaction with diffusing entities. To understand reaction kinetics in these situations, we study the first hitting time statistics of a Brownian particle searching for a target site that switches stochastically between visible and hidden phases. At high crypticity, an unexpected rate limited power-law regime emerges for the first hitting time density, which markedly differs from the classic $t^{-3/2}$ scaling for steady targets. Our problem admits an asymptotic mapping onto a mixed, or Robin, boundary condition. Similar results are obtained with non-Markov targets and particles diffusing anomalously.
We generalize the notion of strong stationary time and we give a representation formula for the hitting time to a target set in the general case of non-reversible Markov processes.
In the setting of non-reversible Markov chains on finite or countable state space, exact results on the distribution of the first hitting time to a given set $G$ are obtained. A new notion of strong metastability time is introduced to describe the lo
For the last ten years, almost every theoretical result concerning the expected run time of a randomized search heuristic used drift theory, making it the arguably most important tool in this domain. Its success is due to its ease of use and its powe
We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a recently propos
The time of the first occurrence of a threshold crossing event in a stochastic process, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the notional senso