Subcritical contact processes seen from a typical infected site
نویسندگان
چکیده
منابع مشابه
Subcritical 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...
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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...
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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.
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We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of the process fall into the absorbing state before the quasi-stationary regime is attained. With relatively modest simulations, the method yields an estimate o...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2014
ISSN: 1083-6489
DOI: 10.1214/ejp.v19-2904