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The Northeast Model is a spin system on the two-dimensional integer lattice that evolves according to the following rule: Whenever a sites southerly and westerly nearest neighbors have spin $1$, it may reset its own spin by tossing a $p$-coin; at all other times, its spin remains frozen. It is proved that the northeast model has a phase transition at $p_{c}=1-beta_{c}$, where $beta_{c}$ is the critical parameter for oriented percolation. For $p<p_{c}$, the trivial measure $delta_{0}$ that puts mass one on the configuration with all spins set at $0$ is the unique ergodic, translation invariant, stationary measure. For $pgeq p_{c}$, the product Bernoulli-$p$ measure on configuration space is the unique nontrivial, ergodic, translation invariant, stationary measure for the system, and it is mixing. For $p>2/3$ it is shown that there is exponential decay of correlations.
Recently, a number of authors have investigated the conditions under which a stochastic perturbation acting on an infinite dimensional dynamical system, e.g. a partial differential equation, makes the system ergodic and mixing. In particular, one is
We consider two approaches to study the spread of infectious diseases within a spatially structured population distributed in social clusters. According whether we consider only the population of infected individuals or both populations of infected i
Various mixing properties of $beta$-, $beta$- and Gaussian Delaunay tessellations in $mathbb{R}^{d-1}$ are studied. It is shown that these tessellation models are absolutely regular, or $beta$-mixing. In the $beta$- and the Gaussian case exponential
Let ${u(t,, x)}_{t >0, x inmathbb{R}}$ denote the solution to the parabolic Anderson model with initial condition $delta_0$ and driven by space-time white noise on $mathbb{R}_+timesmathbb{R}$, and let $bm{p}_t(x):= (2pi t)^{-1/2}exp{-x^2/(2t)}$ denot
We prove that the distribution of eigenvectors of generalized Wigner matrices is universal both in the bulk and at the edge. This includes a probabilistic version of local quantum unique ergodicity and asymptotic normality of the eigenvector entries.