The convex hull for a random acceleration process in two dimensions

Details The convex hull for a random acceleration process in two dimensions The convex hull for a random acceleration process in two dimensions

2011-08-27

arxiv.org/abs/1108.5455v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, 7 figures, accepeted in Journal of Physics A: Mathematical and Theoretical

Scientific paper

We compute exactly the mean perimeter and the mean area of the convex hull of a random acceleration process of duration T in two dimensions. We use an exact mapping that relates, via Cauchy's formulae, the computation of the perimeter and the area of the convex hull of an arbitrary two dimensional stochastic process [x(t); y(t)] to the computation of the extreme value statistics of the associated one dimensional component process x(t). The latter can be computed exactly for the one dimensional random acceleration process even though the process in non-Markovian. Physically, our results are relevant in describing theaverage shape of a semi-flexible ideal polymer chain in two dimensions.

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