Mathematics – Probability
Scientific paper
2006-10-21
Mathematics
Probability
48 pages, revised version, to appear in Ann. Inst. H. Poincare (B) Probab. Statist
Scientific paper
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.
Dawson Don A.
Greven Andreas
Hollander Frank den
Sun Rongfeng
Swart Jan M.
No associations
LandOfFree
The renormalization transformation for two-type branching models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The renormalization transformation for two-type branching models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The renormalization transformation for two-type branching models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-553180