On a Generalization of the Arcsine Law
Christian Houdr\'e, Trevis J. Litherland
TL;DR
This paper explores a generalized version of the Arcsine Law, focusing on the distribution of times when the sum of independent Brownian motions reaches its maximum within a Weyl chamber.
Contribution
It introduces a new generalization of the Arcsine Law related to Brownian motion maxima in Weyl chambers, expanding understanding of their distributional properties.
Findings
The gaps follow a Dirichlet distribution.
Maxima times are characterized within the Weyl chamber.
Generalization extends classical Arcsine Law results.
Abstract
The gaps between the times, in a Weyl chamber, at which the sum of the increments of independent Brownian motions attains its maximum has a Dirichlet distribution.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and statistical mechanics · Bayesian Methods and Mixture Models