Details

Autor(en) / Beteiligte

• Schawe, Hendrik
• Hartmann, Alexander K
• Majumdar, Satya N

Titel

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

Ist Teil von

• Physical review. E, 2017-12, Vol.96 (6-1), p.062101-062101, Article 062101

Ort / Verlag

United States: American Physical Society (APS)

Erscheinungsjahr

2017

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.