The renormalization transformation for two-type branching models

Dawson DA, den Hollander F, Sun R, Swart JM, Greven A (2008)

Publication Type: Journal article, Original article

Publication year: 2008

Journal

Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques Elsevier Masson / Institute Henri Poincaré

Publisher: Elsevier Masson / Institute Henri Poincaré

Book Volume: 44

Pages Range: 1038-1077

URI: https://arxiv.org/abs/math/0610645v2

DOI: 10.1214/07-AIHP143

Abstract

This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting within colonies. Their large-scale space-time behavior can be studied by means of a renormalization program. This program, which has been carried out successfully in a number of other cases (mostly one-dimensional), is based on the construction and the analysis of a nonlinear renormalization transformation, acting on the diffusion function for the components of the system and connecting the evolution of successive block averages on successive time scales. We identify a general class of diffusion functions on the positive quadrant for which this renormalization transformation is well defined and, subject to a conjecture on its boundary behavior, can be iterated. Within certain subclasses, we identify the fixed points for the transformation and investigate their domains of attraction. These domains of attraction constitute the universality classes of the system under space-time scaling. © Association des Publications de l'Institut Henri Poincaré, 2008.

Authors with CRIS profile

Andreas Greven Lehrstuhl für Mathematische Stochastik

Involved external institutions

National University of Singapore (NUS) SG Singapore (SG) Leiden University NL Netherlands (NL)

How to cite

APA:

Dawson, D.A., den Hollander, F., Sun, R., Swart, J.M., & Greven, A. (2008). The renormalization transformation for two-type branching models. Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques, 44, 1038-1077. https://doi.org/10.1214/07-AIHP143

MLA:

Dawson, Donald Andrew, et al. "The renormalization transformation for two-type branching models." Annales de l'Institut Henri Poincaré - Probabilités Et Statistiques 44 (2008): 1038-1077.

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