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Complex Brownian motion representation of the Dyson model

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Complex Brownian motion representation of the Dyson model
2.	Creator	Author's name, affiliation, country	Makoto Katori; Chuo university; Japan
2.	Creator	Author's name, affiliation, country	Hideki Tanemura; Chiba university; Japan
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Dyson model; h-transform; complex Brownian motions; entire functions; conformal martingales; determinantal process; tightness; noncolliding property
3.	Subject	Subject classification	60J70; 60G44; 82C22; 32A15; 15A52
4.	Description	Abstract	Dyson's Brownian motion model with the parameter $\beta=2$, which we simply call the Dyson model in the present paper, is realized as an $h$-transform of the absorbing Brownian motion in a Weyl chamber of type A. Depending on initial configuration with a finite number of particles, we define a set of entire functions and introduce a martingale for a system of independent complex Brownian motions (CBMs), which is expressed by a determinant of a matrix with elements given by the conformal transformations of CBMs by the entire functions. We prove that the Dyson model can be represented by the system of independent CBMs weighted by this determinantal martingale. From this CBM representation, the Eynard-Mehta-type correlation kernel is derived and the Dyson model is shown to be determinantal. The CBM representation is a useful extension of $h$-transform, since it works also in infinite particle systems. Using this representation, we prove the tightness of a series of processes, which converges to the Dyson model with an infinite number of particles, and the noncolliding property of the limit process.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	The Grant-in-Aid for Scientific Research of Japan Society for the Promotion of Science
7.	Date	(YYYY-MM-DD)	2013-01-12
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/2554
10.	Identifier	Digital Object Identifier	10.1214/ECP.v18-2554
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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