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A Representation for Non-Colliding Random Walks

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	A Representation for Non-Colliding Random Walks
2.	Creator	Author's name, affiliation, country	Neil O'Connell; BRIMS, HP Labs
2.	Creator	Author's name, affiliation, country	Marc Yor; Universite Pierre et Marie Curie
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	GUE, eigenvalues of random matrices, Hermitian Brownianmotion, non-colliding Brownian motions, Weyl chamber, queues in series,Burke's theorem, reversibility, Pitman's representation theorem, Charlierensemble.
3.	Subject	Subject classification	15A52, 60J27, 60J65, 60J45, 60K25
4.	Description	Abstract	We define a sequence of mappings $\Gamma_k:D_0(R_+)^k\to D_0(R_+)^k$ and prove the following result: Let $N_1,\ldots,N_n$ be the counting functions of independent Poisson processes on $R_+$ with respective intensities $\mu_1 < \mu_2 < \cdots < \mu_n$. The conditional law of $N_1,\ldots,N_n$, given that $$N_1(t)\le\cdots\le N_n(t), \mbox{ for all }t\ge 0,$$ is the same as the unconditional law of $\Gamma_n(N)$. From this, we deduce the corresponding results for independent Poisson processes of equal rates and for independent Brownian motions (in both of these cases the conditioning is in the sense of Doob).  This extends a recent observation, independently due to Baryshnikov (2001) and Gravner, Tracy and Widom (2001), which relates the law of a certain functional of Brownian motion to that  of the largest eigenvalue of a GUE random matrix.  Our main result can also be regarded as a generalisation of Pitman's representation for the 3-dimensional Bessel process.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2001-07-28
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1042
10.	Identifier	Digital Object Identifier	10.1214/ECP.v7-1042
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 7
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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