Exponential Decay of Correlations for Strongly Coupled Toom Probabilistic Cellular Automata

We investigate the low-noise regime of a large class of probabilistic cellular automata, including the North-East-Center model of Toom. They are defined as stochastic perturbations of cellular automata belonging to the category of monotonic binary tessellations and possessing a property of erosion. We prove, for a set of initial conditions, exponential convergence of the induced processes toward an extremal invariant measure with a highly predominant spin value. We also show that this invariant measure presents exponential decay of correlations in space and in time and is therefore strongly mixing.Comment: 21 pages, 0 figure, revised version including a generalization to a larger class of models, structure of the arguments unchanged, minor changes suggested by reviewers, added reference

Measurement of the differential cross section for the production of an isolated photon with associated jet in ppbar collisions at sqrt(s)=1.96 TeV

The process ppbar -> photon + jet + X is studied using 1.0 fb^-1 of data collected by the D0 detector at the Fermilab Tevatron ppbar collider at a center-of-mass energy sqrt(s)=1.96 TeV. Photons are reconstructed in the central rapidity region |y_gamma|<1.0 with transverse momenta in the range 30<Pt_gamma<400 GeV while jets are reconstructed in either the central |y_jet|15 GeV. The differential cross section d^3sigma/dPt_gamma dy_gamma dy_jet is measured as a function of Pt_gamma in four regions, differing by the relative orientations of the photon and the jet in rapidity. Ratios between the differential cross sections in each region are also presented. Next-to-leading order QCD predictions using different parameterizations of parton distribution functions and theoretical scale choices are compared to the data. The predictions do not simultaneously describe the measured normalization and Pt_gamma dependence of the cross section in any of the four measured regions.Comment: 13 pages, 10 figure