# Robust random search with scale-free stochastic resetting

## TL;DR

This paper introduces a stochastic resetting search model with a rate inversely proportional to time, leading to a paradoxical diffusion process that enhances search efficiency without needing parameter optimization.

## Contribution

It proposes a novel resetting protocol based on scale-free, time-dependent rates, demonstrating its effectiveness across different diffusion regimes.

## Key findings

- Paradoxical diffusion with self-similarity and linear MSD growth.
- Resetting protocol improves search efficiency without parameter tuning.
- Applicable to subdiffusive and superdiffusive regimes.

## Abstract

A new model of search based on stochastic resetting is introduced, wherein rate of resets depends explicitly on time elapsed since the beginning of the process. It is shown that rate inversely proportional to time leads to paradoxical diffusion which mixes self-similarity and linear growth of the mean square displacement with non-locality and non-Gaussian propagator. It is argued that such resetting protocol offers a general and efficient search-boosting method that does not need to be optimized with respect to the scale of the underlying search problem (e.g., distance to the goal) and is not very sensitive to other search parameters. Both subdiffusive and superdiffusive regimes of the mean squared displacement scaling are demonstrated with more general rate functions.