Biased random walk on random networks in presence of stochastic resetting: exact results

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.

Time-dependent probability density function for partial resetting dynamics

“…Aspects of ergodicity restoration in anomalous diffusion processes were also analysed [62]. For SR on networks [63][64][65], the minimisation of global mean first passage times for specific centrality-based SR mechanisms were reported [66]. We note that results similar to SR for a single absorbing target were obtained for multiple as well as partially absorbing targets [67,68].…”

Stochastic resetting in interacting particle systems: a review

“…Over the years, the effects of stochastic resetting have been investigated in a wide spectrum of dynamics, e.g. diffusion [2,[4][5][6][7][8][9][10], random walks [11,12], random walks on disordered lattices [13], Lévy flights [14], Bernoulli trials [15], discrete-time resets [16,17], active motion [18] and transport in cells [19], search problems [14,[20][21][22][23][24][25], RNA-polymerase dynamics [26,27], enzymatic reactions [28], dynamics of ecological systems [29,30], and in discussing Feynman-Kac path integral formalisms [31].…”