Optimizing the random search of a finite-lived target by a Lévy flight

Boyer, Denis; Mercado-Vásquez, Gabriel; Majumdar, Satya N.; Schehr, Grégory

doi:10.1103/physreve.109.l022103

Cited by 1 publication

(1 citation statement)

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“…Stochastic inactivation, which is used to assign a lifespan to a searcher according to a given distribution, can also be used to tune, or sharpen, search process statistics [15][16][17][18][19]. In the work of Ma et al [20] on the role of inactivation in intracellular signalling, inactivation can model degradation, (de)phosphorylation, or other mechanisms that immobilize signal propagation.…”

Section: Introductionmentioning

confidence: 99%

Hitting probabilities for fast stochastic search ^*

Linn,

Lawley

2024

J. Phys. A: Math. Theor.

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Many physical phenomena are modeled as stochastic searchers looking for targets. In these models, the probability that a searcher finds a particular target, its so-called hitting probability, is often of considerable interest. In this work we determine hitting probabilities for stochastic search processes conditioned on being faster than a random short time. Such times have been used to model stochastic resetting or stochastic inactivation. These results apply to any search process, diffusive or otherwise, whose unconditional short-time behavior can be adequately approximated, which we characterize for broad classes of stochastic search. We illustrate these results in several examples and show that the conditional hitting probabilities depend predominantly on the relative geodesic lengths between the initial position of the searcher and the targets. Finally, we apply these results to a canonical evidence accumulation model for decision making.

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