A Generalised Airy Distribution Function for the Accumulated Area Swept by N Vicious Brownian Paths

In this work exact expressions for the distribution function of the accumulated area swept by excursions and meanders of N vicious Brownian particles up to time T are derived. The results are expressed in terms of a generalised Airy distribution function, containing the Vandermonde determinant of th...

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Veröffentlicht in:	Journal of statistical physics 2016-03, Vol.162 (6), p.1587-1607
Hauptverfasser:	Castillo, Isaac Pérez, Boyer, Denis
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematical and Computational Physics Monte Carlo method Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	In this work exact expressions for the distribution function of the accumulated area swept by excursions and meanders of N vicious Brownian particles up to time T are derived. The results are expressed in terms of a generalised Airy distribution function, containing the Vandermonde determinant of the Airy roots. By mapping the problem to an Random Matrix Theory ensemble we are able to perform Monte Carlo simulations finding perfect agreement with the theoretical results.
ISSN:	0022-4715 1572-9613
DOI:	10.1007/s10955-016-1467-2