Open Problem/Discussion: Biased random walks on random networks: How space heterogeneity impacts transport properties

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• Shamik Gupta (Tata Institute of Fundamental Research)
• Tuesday 15 August 2023, 11:15-12:00
• Seminar Room 2, Newton Institute.

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MMV - Mathematics of movement: an interdisciplinary approach to mutual challenges in animal ecology and cell biology

In the context of transport in heterogeneous space, we study biased random walkers on random networks constituted by a random comb that has a backbone with quenched-disordered random-length branches. The consequences are drastic: the drift velocity of the walkers varies non-monotonically as a function of the bias, and it becomes zero beyond a critical bias ! We demonstrate these effects on the basis of exact results for the stationary state for any disorder realization of branch lengths sampled following an arbitrary distribution. We derive along the way a criterion for observing a non-monotonic drift velocity. Further, we show that stochastic resetting of walkers from branches to the backbone allows the system to have a drift velocity that is finite at any bias.

This talk is part of the Isaac Newton Institute Seminar Series series.

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