Palm pairs and the general mass-transport principle

We consider a lcsc group G acting properly on a Borel space S and measurably on an underlying sigma-finite measure space. Our first main result is a transport formula connecting the Palm pairs of jointly stationary random measures on S. A key (and new) technical result is a measurable disintegration of the Haar measure on G along the orbits. The second main result is an intrinsic characterization of the Palm pairs of a G-invariant random measure. We then proceed with deriving a general version of the mass-transport principle for possibly non-transitive and non-unimodular group operations first in a deterministic and then in its full probabilistic form.Comment: 26 page

Decorrelation of a class of Gibbs particle processes and asymptotic properties of U-statistics

We study a stationary Gibbs particle process with deterministically bounded particles on Euclidean space defined in terms of an activity parameter and non-negative interaction potentials of finite range. Using disagreement percolation we prove exponential decay of the correlation functions, provided a dominating Boolean model is subcritical. We also prove this property for the weighted moments of a U-statistic of the process. Under the assumption of a suitable lower bound on the variance, this implies a central limit theorem for such U-statistics of the Gibbs particle process. A byproduct of our approach is a new uniqueness result for Gibbs particle processes

Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization

We prove a new class of inequalities, yielding bounds for the normal approximation in the Wasserstein and the Kolmogorov distance of functionals of a general Poisson process (Poisson random measure). Our approach is based on an iteration of the classical Poincaré inequality, as well as on the use of Malliavin operators, of Stein’s method, and of an (integrated) Mehler’s formula, providing a representation of the Ornstein-Uhlenbeck semigroup in terms of thinned Poisson processes. Our estimates only involve first and second order difference operators, and have consequently a clear geometric interpretation. In particular we will show that our results are perfectly tailored to deal with the normal approximation of geometric functionals displaying a weak form of stabilization, and with non-linear functionals of Poisson shot-noise processes. We discuss two examples of stabilizing functionals in great detail: (i) the edge length of the k-nearest neighbour graph, (ii) intrinsic volumes of k-faces of Voronoi tessellations. In all these examples we obtain rates of convergence (in the Kolmogorov and the Wasserstein distance) that one can reasonably conjecture to be optimal, thus significantly improving previous findings in the literature. As a necessary step in our analysis, we also derive new lower bounds for variances of Poisson functionals

Religião e controle social no mundo romano: a proibição das Bacanais em 186 a.C. Conferência do I Colóquio Internacional e III Colóquio Nacional do LEIR (Laboratório de estudos sobre o Império Romano) da Universidade Estadual Paulista Júlio de Mesquita Filho (UNESP), Campus Franca. Setembro de 2010

No ano de 186 a.C. foram duramente reprimidos os cultos báquicos na Itália por meio de diferentes medidas tomadas pelo senado (senatus consultum de Bacchanalibus ,CIL I2 581 e Liv. 39, 8-19). Uma extensa tradição historiográfica moderna afirma que a proibição deste culto constitui "um fato absolutamente excepcional na história de Roma", pois o paganismo se caracterizou pela abertura e a tolerância. No entanto, o tema da tolerância religiosa em sistemas politeístas é bastante complexo (Rüpke 2001) e não se trata de uma simples exceção, como o manifestou North em seu estudo sobre a tolerância religiosa na república romana (North 1979). Nesta perspectiva, o estudo das fontes da proibição das bacanais em Roma no ano de 186 a.C. e sua recepção (Lívio) oferece um ponto de referência para o tema da relação entre religião, ordem, estrutura, disciplinamento e controle social no mundo romano. Esse é o marco no qual se pode contextualizar a discussão sobre tolerância e intolerância religiosa na república romana