Title:	Proxitaxis: An adaptive search strategy based on proximity and stochastic resetting
Authors:	Del Vecchio Del Vecchio, Giuseppe Kulkarni, Manas Majumdar, Satya N Sabhapandit, Sanjib
Keywords:	Brownian motion Diffusion Search strategy Stochastic resetting Fokker–Planck equation
Issue Date:	2-Apr-2026
Publisher:	Physical Review E
Citation:	Physical Review E, 2026, Vol. 113 (4), AR No. L042101
Abstract:	We introduce proxitaxis, a simple search strategy where the searcher has only information about the distance from the target but not the direction. The strategy consists of three crucial components: (i) local adaptive moves with a distance-dependent diffusion coefficient, (ii) intermittent long-range returns via stochastic resetting to a certain location 𝑅0, and (iii) an inspection move where the searcher dynamically updates the resetting position ⃗𝑅0. We compute analytically the capture probability of the target within this strategy and show that it can be maximized by an optimal choice of the control parameters of this strategy. Moreover, the optimal strategy undergoes multiple phase transitions as a function of the control parameters. These phase transitions are generic and occur in all dimensions.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/8703
ISSN:	2470-0053
Alternative Location:	https://doi.org/10.48550/arXiv.2507.05800 https://doi.org/10.1103/bjl2-kmrt
Copyright:	©2026 American Physical Society
Appears in Collections:	Research Papers (TP)

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