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**Harvard**

Broman, E. (2006) *Interacting Particle Systems: Percolation, Stochastic Domination and Randomly Evolving Environments*. Göteborg : Chalmers University of Technology (Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, nr: 2444).

** BibTeX **

@book{

Broman2006,

author={Broman, Erik},

title={Interacting Particle Systems: Percolation, Stochastic Domination and Randomly Evolving Environments},

isbn={91-7291-762-8},

abstract={In this thesis we first analyze the class of one-dependent trigonometric
determinantal processes and show that they are all two-block-factors. We do this by constructing
the two-block-factors explicitly.
Second we investigate the dynamic stability of percolation for the stochastic Ising model and the contact process.
This is a natural extension of what previously has been done for non-interacting particle systems. The main question we ask is:
If we have percolation at a fixed time in a time-dependent but time-invariant
system, do we have percolation at all times? A key tool in the
analysis is the concept of $\epsilon-$movability which we introduce here. We then proceed by developing and
relating this concept to others previously studied.
Finally, we introduce a new model which we refer to as the contact process in a randomly evolving environment.
By using stochastic domination techniques we will investigate matters of extinction and that
of weak and strong survival for this system. We do this by establishing stochastic relations
between our new model and the ordinary contact process. In the process, we develop some sharp stochastic
domination results for a hidden Markov chain and a continuous time analogue of this.
},

publisher={Institutionen för matematiska vetenskaper, matematik, Chalmers tekniska högskola,},

place={Göteborg},

year={2006},

series={Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 2444},

keywords={Determinantal processes, k-dependence, k-block-factors, percolation, stochastic Ising models, contact process, $\epsilon-$movability, hidden Markov chain, stochastic domination},

note={125},

}

** RefWorks **

RT Dissertation/Thesis

SR Electronic

ID 19646

A1 Broman, Erik

T1 Interacting Particle Systems: Percolation, Stochastic Domination and Randomly Evolving Environments

YR 2006

SN 91-7291-762-8

AB In this thesis we first analyze the class of one-dependent trigonometric
determinantal processes and show that they are all two-block-factors. We do this by constructing
the two-block-factors explicitly.
Second we investigate the dynamic stability of percolation for the stochastic Ising model and the contact process.
This is a natural extension of what previously has been done for non-interacting particle systems. The main question we ask is:
If we have percolation at a fixed time in a time-dependent but time-invariant
system, do we have percolation at all times? A key tool in the
analysis is the concept of $\epsilon-$movability which we introduce here. We then proceed by developing and
relating this concept to others previously studied.
Finally, we introduce a new model which we refer to as the contact process in a randomly evolving environment.
By using stochastic domination techniques we will investigate matters of extinction and that
of weak and strong survival for this system. We do this by establishing stochastic relations
between our new model and the ordinary contact process. In the process, we develop some sharp stochastic
domination results for a hidden Markov chain and a continuous time analogue of this.

PB Institutionen för matematiska vetenskaper, matematik, Chalmers tekniska högskola,

T3 Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 2444

LA eng

LK http://www.math.chalmers.se/Math/Research/Preprints/Doctoral/2006/1.pdf

OL 30