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 Electronic Journal of Probability > Vol. 7 (2002) > Paper 7 open journal systems 


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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Pages: 1-57

Published on: December 3, 2001
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Electronic Journal of Probability. ISSN: 1083-6489