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Journal Article

Diffusion with stochastic resetting at power-law times

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Gupta,  Shamik
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Nagar, A., & Gupta, S. (2016). Diffusion with stochastic resetting at power-law times. Physical Review E, 93(6): 060102. doi:10.1103/PhysRevE.93.060102.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002A-F8F6-5
Abstract
What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals tau distributed as a power law similar to tau(-(1+alpha)); alpha > 0? Modeling the stochastic process by diffusion and the large changes as abrupt resets to the initial condition, we obtain exact closed-form expressions for both static and dynamic quantities, while accounting for strong correlations implied by a power law. Our results show that the resulting dynamics exhibits a spectrum of rich long-time behavior, from an ever-spreading spatial distribution for alpha < 1, to one that is time independent for alpha > 1. The dynamics has strong consequences on the time to reach a distant target for the first time; we specifically show that there exists an optimal alpha that minimizes the mean time to reach the target, thereby offering a step towards a viable strategy to locate targets in a crowded environment.