Phase transitions in optimal search times: How random walkers should combine resetting and flight scales

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
D Campos, V Méndez

Abstract

Recent works have explored the properties of Lévy flights with resetting in one-dimensional domains and have reported the existence of phase transitions in the phase space of parameters which minimizes the mean first passage time (MFPT) through the origin [L. Kusmierz et al., Phys. Rev. Lett. 113, 220602 (2014)]. Here, we show how actually an interesting dynamics, including also phase transitions for the minimization of the MFPT, can also be obtained without invoking the use of Lévy statistics but for the simpler case of random walks with exponentially distributed flights of constant speed. We explore this dynamics both in the case of finite and infinite domains, and for different implementations of the resetting mechanism to show that different ways to introduce resetting consistently lead to a quite similar dynamics. The use of exponential flights has the strong advantage that exact solutions can be obtained easily for the MFPT through the origin, so a complete analytical characterization of the system dynamics can be provided. Furthermore, we discuss in detail how the phase transitions observed in random walks with resetting are closely related to several ideas recurrently used in the field of random search theory, in partic...Continue Reading

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Dec 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel CamposVicenç Méndez

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Citations

Nov 28, 2019·Physical Review. E·Axel Masó-PuigdellosasVicenç Méndez
Jul 18, 2018·Physical Review. E·Abhinava ChatterjeeAndreas Schadschneider
Oct 24, 2019·Physical Review. E·Łukasz Kuśmierz, Taro Toyoizumi
Aug 17, 2020·Physical Review Letters·B De BruyneS Redner
Jul 15, 2016·Physical Review. E·Apoorva Nagar, Shamik Gupta
Mar 18, 2016·Physical Review. E·Vicenç Méndez, Daniel Campos
Feb 6, 2019·Physical Review Letters·Arnab PalShlomi Reuveni
Aug 18, 2018·Physical Review Letters·A Chechkin, I M Sokolov
Feb 20, 2019·Physical Review. E·Axel Masó-PuigdellosasVicenç Méndez
Apr 20, 2019·Physical Review. E·Arnab Pal, V V Prasad
Jun 20, 2019·Physical Review. E·Łukasz Kuśmierz, Ewa Gudowska-Nowak
Jun 18, 2021·Physical Review. E·Marcus DahlenburgRalf Metzler

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