Large deviations of convex hulls of self-avoiding random walks

Hendrik Schawe, Alexander K. Hartmann, and Satya N. Majumdar
Phys. Rev. E 97, 062159 – Published 29 June 2018

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=10100. 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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  • Received 9 April 2018
  • Revised 18 June 2018

DOI:https://doi.org/10.1103/PhysRevE.97.062159

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Hendrik Schawe* and Alexander K. Hartmann

  • Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany and LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

Satya N. Majumdar

  • LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

  • *hendrik.schawe@uni-oldenburg.de
  • a.hartmann@uni-oldenburg.de
  • satya.majumdar@u-psud.fr

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Issue

Vol. 97, Iss. 6 — June 2018

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