The convex hull for a random acceleration process in two dimensions

Abstract

We compute exactly the mean perimeter <L(T)> and the mean area <A(T)> 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.

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

References in corpus (5)

• Random Convex Hulls and Extreme Value Statistics
• Convex Hull of N Planar Brownian Motions: Exact Results and an Application to Ecology
• Time to reach the maximum for a random acceleration process
• Extreme statistics for time series: Distribution of the maximum relative to the initial value
• Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation

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