The Contact Process Seen from a Typical Infected Site
نویسندگان
چکیده
منابع مشابه
The contact process seen from a typical infected site
This paper considers contact processes on general lattices. Assuming that the expected number of infected sites grows subexponentially, it is shown that the configuration as seen from a typical (‘Palmed’) infected site at an exponentially distributed time converges, as time tends to infinity, to the upper invariant law conditioned on the origin being infected. The assumption that the expected n...
متن کاملThe contact process seen from a typical infected site Jan
We consider contact processes on general Cayley graphs. It is shown that any such contact process has a well-defined exponential growth rate, which can be related to the configuration seen from a ‘typical’ infected site at a ‘typical’ late time. Using this quantity, it is proved that on any nonamenable Cayley graph, the critical contact process dies out.
متن کاملThe Contact Process Seen from a Typical Infected Site. Contents
This paper studies contact processes on general countable groups. It is shown that any such contact process has a well-defined exponential growth rate, and this quantity is used to study the process. In particular, it is proved that on any nonamenable group, the critical contact process dies out.
متن کاملSubcritical Contact Processes Seen from a Typical Infected Site *
What is the long-time behavior of the law of a contact process started with a single infected site, distributed according to counting measure on the lattice? This question is related to the configuration as seen from a typical infected site and gives rise to the definition of so-called eigenmeasures, which are possibly infinite measures on the set of nonempty configurations that are preserved u...
متن کاملThe critical contact process seen from the right edge
Durret t (1984) proved the existence of an invariant measure for the critical and supercritical contact process seen from the right edge. Galves and Presutti (1987) proved, in the supercritical case, that the invariant measure was unique, and convergence to it held starting in any semi-infinite initial state. We prove the same for the critical contact process. We also prove that the process sta...
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2008
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-008-0184-4