Thomas Mountford (EPFL, Lausanne)
 
Critical values for threshold contact processes in large dimensions.
(joint work with Roberto Schonmann)
 
We consider spin systems on $\{0,1\}^{Z^d}$ where spins of value $1$ change to spins of value $0$ at rate $1$ irrespetive of the surrounding configuration but for which $0$'s change to $1$'s at rate $\lambda$ only if at least $r$ neighbouring values are $1$ where $r \leq d$.  The system is attractive and thus two critical values are well defined: the value $\lambda$ above which there exist non trivial equilibria for the system the value $\lambda$ such that if the system begins from product measure with a strictly positive density then the system does not die out (in an obvious sense).
 
We show that both parameters tend to zero as $d$ tends to infinity.
 
The work follows earlier work of Toom, Chen, Fontes, Sidoravicius and Schonmann and Fontes and Schonmann.

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