Title:	First order transition for the optimal search time of lévy flights with resetting
Authors:	Kusmierz, Lukasz Majumdar, Satya N. Sabhapandit, Sanjib Schehr, Gregory
Issue Date:	28-Nov-2014
Publisher:	American Physical Society
Citation:	Physical Review Letters, 2014, Vol. 113, p 220602
Abstract:	We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at x0≥0, where successive jumps are drawn independently from an arbitrary jump distribution f(η). In addition, with a probability 0≤r<1, the position of the searcher is reset to its initial position x0. The efficiency of the search strategy is characterized by the mean time to find the target, i.e., the mean first passage time (MFPT) to the origin. For arbitrary jump distribution f(η), initial position x0 and resetting probability r, we compute analytically the MFPT. For the heavy-tailed Lévy stable jump distribution characterized by the Lévy index 0<μ<2, we show that, for any given x0, the MFPT has a global minimum in the (μ,r) plane at (μ∗(x0),r∗(x0)). We find a remarkable first-order phase transition as x0 crosses a critical value x∗0 at which the optimal parameters change discontinuously. Our analytical results are in good agreement with numerical simulations.
Description:	Open Access
URI:	http://hdl.handle.net/2289/6239
ISSN:	1079-7114 1079-7114(Online)
Alternative Location:	http://arxiv.org/abs/1409.1733 http://dx.doi.org/10.1103/PhysRevLett.113.220602 http://adsabs.harvard.edu/abs/2014PhRvL.113v0602K
Copyright:	2014 American Physical Society
Appears in Collections:	Research Papers (TP)

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