Large deviations of convex hulls of self-avoiding random walks

Physical Review. E
Hendrik SchaweSatya N Majumdar

Abstract

A global picture of a random particle movement is given by the convex hull of the visited points. We obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of self-avoiding random walks, namely, the classical self-avoiding walk, the smart-kinetic self-avoiding walk, and the loop-erased random walk. To obtain a comprehensive description of the measured random quantities, we applied sophisticated large-deviation techniques, which allowed us to obtain the distributions over a large range of support down to probabilities far smaller than P=10^{-100}. We give an approximate closed form of the so-called large-deviation rate function Φ which generalizes above the upper critical dimension to the previously studied case of the standard random walk. Further, we show correlations between the two observables also in the limits of atypical large or small values.

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Jan 20, 2018·Physical Review. E·Hendrik SchaweSatya N Majumdar

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Citations

Jan 23, 2020·Physical Review. E·Urna BasuGrégory Schehr
Jul 22, 2020·Physical Review. E·Phil KrabbeAlexander K Hartmann
Jan 21, 2021·Physical Review. E·Hendrik Schawe, Alexander K Hartmann
Dec 18, 2020·Physical Review. E·Hendrik Schawe, Alexander K Hartmann
Feb 20, 2021·Physical Review. E·David S DeanHendrik Schawe

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