Journal of Statistical Physics

, Volume 162, Issue 6, pp 1587–1607 | Cite as

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

  • Isaac Pérez Castillo
  • Denis Boyer


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.


Random walkers Vicious walkers Random matrices  Airy distribution function 



The authors warmly thank N. Kobayashi and M. Katori for email correspondence regarding the simulations. We also thank E. Barkai for pointing out some references.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Departamento de Sistemas ComplejosInstituto de Física, UNAMMexicoMexico

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