MPEJ Volume 11, No. 3, 52 pp.
Received: Jul 7, 2004. Revised: Jul 26, 2005. Accepted:  Sep 1, 2005.

R. Fernandez, P.A. Ferrari and G. Guerberoff
Spatial birth-and-dead processes in random environment

ABSTRACT:  We consider birth-and-death processes of objects (animals)
defined in $\Z^d$ 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 Klein
to establish conditions for the absence of percolation.

http://www.maia.ub.es/mpej/Vol/11/3.ps
http://www.maia.ub.es/mpej/Vol/11/3.pdf

http://www.ma.utexas.edu/mpej/Vol/11/3.ps
http://www.ma.utexas.edu/mpej/Vol/11/3.pdf

http://mpej.unige.ch/mpej/Vol/11/3.ps
http://mpej.unige.ch/mpej/Vol/11/3.pdf