Renormalizations of Branching Random Walks in Equilibrium
Iljana Zähle, Universität Erlangen-Nürnberg
Abstract
We study the d-dimensional branching random walk for d>2.
This process has extremal equilibria for every intensity. We are interested in
the large space scale and large space-time scale behavior of the equilibrium
state. We show that the fluctuations of space and space-time averages with a
non-classical scaling are Gaussian in the limit. For this purpose we use the
historical process, which allows a family decomposition. To control the
distribution of the families we use the concept of canonical measures and Palm
distributions.
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