Biased random walk on random networks in presence of stochastic resetting: exact results. (21st October 2022)

• Record Type: Journal Article
• Authors: Sarkar, Mrinal; Gupta, Shamik
• Is Part Of: Journal of physics. Volume 55:Number 42(2022)
• Publication Date: 2022-10-21
• Subjects: stochastic resetting -- random walk -- nonequilibrium stationary state; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac9656
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as also when the model is subject to stochastic resetting, whereby the walkers on the branches reset with a constant rate to the respective backbone sites, we obtain exact stationary-state static and dynamic properties for a given disorder realization of branch lengths sampled following an arbitrary distribution. We derive a criterion to observe in the stationary state a non-zero drift velocity along the backbone. For the bare model, we discuss the occurrence of a drift velocity that is non-monotonic as a function of the bias, becoming zero beyond a threshold bias because of walkers trapped at very long branches. Further, we show that resetting allows the system to escape trapping, resulting in a drift velocity that is finite at any bias.