Particle systems with quasi-homogeneous initial states and their occupation time fluctuations
Tomasz Bojdecki, Institute of Mathematics, University of Warsaw
Luis G. Gorostiza, Centro de Investigacion y de Estudios Avanzados, Mexico
Anna Talarczyk, Institute of Mathematics, University of Warsaw
Abstract
We consider particle systems in R with initial configurations belonging to a class of measures that obey a quasi-homogeneity property, which includes as special cases homogeneous Poisson measures and many deterministic measures (simple example: one atom at each point of Z). The particles move independently according to an alpha-stable Levy process, alpha>1, and we also consider the model where they undergo critical branching. Occupation time fluctuation limits of such systems have been studied in the Poisson case. For the branching system in ``low'' dimension the limit was characterized by a process called sub-fractional Brownian motion, and this process was attributed to the branching because it had appeared only in that case. In the present more general framework sub-fractional Brownian motion is more prevalent, namely, it also appears as a component of the limit for the system without branching in ``low'' dimension. A new method of proof, based on the central limit theorem, is used.
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