@article{EJP341,
author = {Jan Swart and Klaus Fleischmann},
title = {Renormalization analysis of catalytic Wright-Fisher diffusions},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {11},
year = {2006},
keywords = {Renormalization, catalytic Wright-Fisher diffusion, embedded particle system, extinction, unbounded growth, interacting diffusions, universality.},
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.},
pages = {no. 24, 585-654},
issn = {1083-6489},
doi = {10.1214/EJP.v11-341},
url = {http://ejp.ejpecp.org/article/view/341}}