Abstract
We study the $d$-dimensional branching random walk for $d \gt 2$. 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.
Citation
Iljana Zähle. "Renormalizations of Branching Random Walks in Equilibrium." Electron. J. Probab. 7 1 - 57, 2002. https://doi.org/10.1214/EJP.v7-106
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