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Interacting particle systems in a randomly evolving environment

Marcus Warfheimer (Institutionen för matematiska vetenskaper, matematik)
Göteborg : Chalmers University of Technology, 2007. - 72 s.
[Licentiatavhandling]

This thesis concerns interacting particle systems in a randomly evolving environment. In the first paper, we consider the so called contact process in a randomly evolving environment (CPREE), introduced by Erik Broman. This process is a generalization of the contact process where the recovery rate can vary between two values. The rate which it chooses is determined by a background process, which evolves independently at different sites. As for the contact process, we can similarly define a critical value in terms of survival for this process. We prove that this definition is independent of how we start the background process, that finite and infinite survival (meaning nontriviality of the upper invariant measure) are equivalent and finally that the process dies out at criticality. In the second paper, we consider spin systems on the integers (i.e. interacting particle systems on the integers in which each coordinate has only two possible values and only one coordinate changes in each transition) whose rates are determined by a background process, which is more general than in the first paper. We prove a generalization of a result by Liggett, that under certain conditions on the rates there are only two extremal invariant distributions.

Nyckelord: Interacting particle systems, contact process, randomly evloving environment, spin systems



Denna post skapades 2007-12-18. Senast ändrad 2007-12-18.
CPL Pubid: 63338

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Annan matematik

Chalmers infrastruktur

Examination

Datum: 2008-01-18
Tid: 10:15
Lokal: Mathematical sciences, room Pascal
Opponent: Olle Häggström