Convex hulls of random walks in higher dimensions: A large-deviation study

The distribution of the hypervolume V and surface ∂V of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than P=10^{-1000} to estimate large deviation properties. For arbitrary dimensions and large walk lengths T...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. E 2017-12, Vol.96 (6-1), p.062101-062101, Article 062101
Main Authors: Schawe, Hendrik, Hartmann, Alexander K, Majumdar, Satya N
Format: Article
Language:English
Subjects:
Condensed Matter
Data Analysis, Statistics and Probability
Physics
Statistical Mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The distribution of the hypervolume V and surface ∂V of convex hulls of (multiple) random walks in higher dimensions are determined numerically, especially containing probabilities far smaller than P=10^{-1000} to estimate large deviation properties. For arbitrary dimensions and large walk lengths T, we suggest a scaling behavior of the distribution with the length of the walk T similar to the two-dimensional case and behavior of the distributions in the tails. We underpin both with numerical data in d=3 and d=4 dimensions. Further, we confirm the analytically known means of those distributions and calculate their variances for large T.
ISSN:2470-0045
2470-0053
DOI:10.1103/physreve.96.062101