Distribution of the area enclosed by a 2D random walk in a disordered medium
K.V. Samokhin (Cavendish Laboratory, University of Cambridge, UK)
TL;DR
This paper calculates the long-term probability distribution of the area enclosed by a 2D Brownian particle moving through a disordered medium with traps, using advanced instanton methods.
Contribution
It introduces a novel application of instanton techniques to derive the asymptotic area distribution in a disordered 2D environment.
Findings
Derived the asymptotic distribution for enclosed area A
Applied instanton techniques to a disordered medium
Provided insights into the behavior of Brownian particles in traps
Abstract
The asymptotic probability distribution for a Brownian particle wandering in a 2D plane with random traps to enclose the algebraic area A by time t is calculated using the instanton technique.
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