Convex hulls of random walks in higher dimensions: A large-deviation study.
basic_science · Level V
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- Record sourced from PubMed, PMID 29347304.
- Also identified by DOI 10.1103/PhysRevE.96.062101.
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Abstract
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.