publication . Article . Preprint . 2004

Spatial birth-and-death processes in random environment

Fernández, R.; Pablo A Ferrari; Guerberoff, G. R.;
Open Access
  • Published: 07 Oct 2004
We consider birth-and-death processes of objects (animals) defined in ${\bf Z}^d$ having unit death rates and random birth rates. For animals with uniformly bounded diameter we establish conditions on the rate distribution under which the following holds for almost all realizations of the birth rates: (i) the process is ergodic with at worst power-law time mixing; (ii) the unique invariant measure has exponential decay of (spatial) correlations; (iii) there exists a perfect-simulation algorithm for the invariant measure. The results are obtained by first dominating the process by a backwards oriented percolation model, and then using a multiscale analysis due to...
free text keywords: Mathematics - Probability, Mathematical Physics, 60K37, 60K35

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