Biased random walks with finite mean first passage time

Christin Puthur; Prabha Chuphal; Snigdha Thakur; Auditya Sharma

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arXiv · 1807.07791

Biased random walks with finite mean first passage time

Christin Puthur·Prabha Chuphal·Snigdha Thakur·Auditya Sharma

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Abstract

A power-law distance-dependent biased random walk model with a tuning parameter ($\sigma$) is introduced in which finite mean first passage times are realizable if $\sigma$ is less than a critical value $\sigma_c$. We perform numerical simulations in $1$-dimension to obtain $\sigma_c \sim 1.14$. The three-dimensional version of this model is related to the phenomenon of chemotaxis. Diffusiophoretic theory supplemented with coarse-grained simulations establish the connection with the specific value of $\sigma = 2$ as a consequence of in-built solvent diffusion. A variant of the one-dimensional power-law model is found to be applicable in the context of a stock investor devising a strategy for extricating their portfolio out of loss.

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Christin Puthur, Prabha Chuphal, Snigdha Thakur, Auditya Sharma. 2018-07-20. Biased random walks with finite mean first passage time. https://arxiv.org/abs/1807.07791

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