Abstract
We consider a Markov chain with values in [0,$\infty$)$^{\mathbb{z}d}$. The Markov chain includes some interesting examples such as the oriented site percolation, the directed polymers in random environment, and a time discretization of the binary contact process. We prove a central limit theorem for “the spatial distribution of population” when $d\geq 3$ and a certain square-integrability condition for the total population is satisfied. This extends a result known for the directed polymers in random environment to a large class of models.
Citation
Makoto Nakashima. "Central Limit Theorem for Linear Stochastic Evolutions." J. Math. Kyoto Univ. 49 (1) 201 - 224, 2009. https://doi.org/10.1215/kjm/1248983037
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