Two Bessel Bridges Conditioned Never to Collide, Double Dirichlet Series, and Jacobi Theta Function

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dc.creatorKatori, Makoto
dc.creatorIzumi, Minami
dc.creatorKobayashi, Naoki
dc.date2007-11-12
dc.date2008-03-13
dc.date.accessioned2026-07-07T11:48:40Z
dc.date.available2026-07-07T11:48:40Z
dc.descriptionIt is known that the moments of the maximum value of a one-dimensional conditional Brownian motion, the three-dimensional Bessel bridge with duration 1 started from the origin, are expressed using the Riemann zeta function. We consider a system of two Bessel bridges, in which noncolliding condition is imposed. We show that the moments of the maximum value is then expressed using the double Dirichlet series, or using the integrals of products of the Jacobi theta functions and its derivatives. Since the present system will be provided as a diffusion scaling limit of a version of vicious walker model, the ensemble of 2-watermelons with a wall, the dominant terms in long-time asymptotics of moments of height of 2-watermelons are completely determined. For the height of 2-watermelons with a wall, the average value was recently studied by Fulmek by a method of enumerative combinatorics.
dc.descriptionv2: LaTeX, 19 pages, 2 figures, minor corrections made for publication in J. Stat. Phys
dc.identifierhttps://arxiv.org/abs/0711.1710
dc.identifierhttp://arxiv.org/abs/0711.1710
dc.identifierJ.Stat.Phys.131:1067-1083,2008
dc.identifierdoi:10.1007/s10955-008-9524-0
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/202962
dc.subjectProbability
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectCombinatorics
dc.subjectExactly Solvable and Integrable Systems
dc.titleTwo Bessel Bridges Conditioned Never to Collide, Double Dirichlet Series, and Jacobi Theta Function
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