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**Harvard**

Liggett, T. och Steif, J. (2006) *Stochastic Domination: The Contact Process, Ising Models and FKG Measures *.

** BibTeX **

@article{

Liggett2006,

author={Liggett, Thomas and Steif, Jeffrey},

title={Stochastic Domination: The Contact Process, Ising Models and FKG Measures },

journal={Annales Institut Henri Poincare, Probabilites et Statistiques},

volume={42},

pages={223-243},

abstract={We prove for the contact process on $Z^d$, and many other graphs, that the upper invariant
measure dominates a homogeneous product measure with large density if the infection rate
$\lambda$ is sufficiently large. As a consequence, this measure percolates if the corresponding
product measure percolates. We raise the question of whether domination holds in the symmetric
case for all infinite graphs of bounded degree. We study some asymmetric examples which we
feel shed some light on this question. We next obtain necessary and sufficient conditions for
domination of a product measure for ``downward'' FKG measures. As a consequence of this
general result, we show that the plus and minus states for the Ising model on $Z^d$ dominate
the same set of product measures. We show that this latter fact fails completely on the homogenous
3-ary tree. We also provide a different distinction between $Z^d$ and the homogenous 3-ary tree
concerning stochastic domination and Ising models; while it is known that the plus states for
different temperatures on $Z^d$ are never stochastically ordered, on the homogenous 3-ary tree,
almost the complete opposite is the case. Next, we show that on $Z^d$, the set of product measures
which the plus state for the Ising model dominates is strictly increasing in the temperature. Finally,
we obtain a necessary and sufficient condition for a finite number of variables, which are both FKG
and exchangeable, to dominate a given product measure. },

year={2006},

keywords={stochastic domination, Ising models, contact process},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 24582

A1 Liggett, Thomas

A1 Steif, Jeffrey

T1 Stochastic Domination: The Contact Process, Ising Models and FKG Measures

YR 2006

JF Annales Institut Henri Poincare, Probabilites et Statistiques

VO 42

SP 223

OP 243

AB We prove for the contact process on $Z^d$, and many other graphs, that the upper invariant
measure dominates a homogeneous product measure with large density if the infection rate
$\lambda$ is sufficiently large. As a consequence, this measure percolates if the corresponding
product measure percolates. We raise the question of whether domination holds in the symmetric
case for all infinite graphs of bounded degree. We study some asymmetric examples which we
feel shed some light on this question. We next obtain necessary and sufficient conditions for
domination of a product measure for ``downward'' FKG measures. As a consequence of this
general result, we show that the plus and minus states for the Ising model on $Z^d$ dominate
the same set of product measures. We show that this latter fact fails completely on the homogenous
3-ary tree. We also provide a different distinction between $Z^d$ and the homogenous 3-ary tree
concerning stochastic domination and Ising models; while it is known that the plus states for
different temperatures on $Z^d$ are never stochastically ordered, on the homogenous 3-ary tree,
almost the complete opposite is the case. Next, we show that on $Z^d$, the set of product measures
which the plus state for the Ising model dominates is strictly increasing in the temperature. Finally,
we obtain a necessary and sufficient condition for a finite number of variables, which are both FKG
and exchangeable, to dominate a given product measure.

LA eng

DO 10.1016/j.anihpb.2005.04.002

LK http://dx.doi.org/10.1016/j.anihpb.2005.04.002

OL 30