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Renormalization analysis of catalytic Wright-Fisher diffusions

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1.	Title	Title of document	Renormalization analysis of catalytic Wright-Fisher diffusions
2.	Creator	Author's name, affiliation, country	Jan M. Swart; UTIA
2.	Creator	Author's name, affiliation, country	Klaus Fleischmann; WIAS Berlin
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Renormalization, catalytic Wright-Fisher diffusion, embedded particle system, extinction, unbounded growth, interacting diffusions, universality.
3.	Subject	Subject classification	82C28;82C22;60J60;60J80
4.	Description	Abstract	Recently, several authors have studied maps where a function, describing the local diffusion matrix of a diffusion process with a linear drift towards an attraction point, is mapped into the average of that function with respect to the unique invariant measure of the diffusion process, as a function of the attraction point. Such mappings arise in the analysis of infinite systems of diffusions indexed by the hierarchical group, with a linear attractive interaction between the components. In this context, the mappings are called renormalization transformations. We consider such maps for catalytic Wright-Fisher diffusions. These are diffusions on the unit square where the first component (the catalyst) performs an autonomous Wright-Fisher diffusion, while the second component (the reactant) performs a Wright-Fisher diffusion with a rate depending on the first component through a catalyzing function. We determine the limit of rescaled iterates of renormalization transformations acting on the diffusion matrices of such catalytic Wright-Fisher diffusions.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Work sponsered through a number of grants of the German Science Foundation, and by the Czech Science Foundation (GAv CR grant 201/06/1323). The second author thanks the Weierstrass Institute for its hospitality in August 2004.
7.	Date	(YYYY-MM-DD)	2006-08-03
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/341
10.	Identifier	Digital Object Identifier	10.1214/EJP.v11-341
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 11
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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