2,636 research outputs found
Empirical Processes of Multidimensional Systems with Multiple Mixing Properties
We establish a multivariate empirical process central limit theorem for
stationary -valued stochastic processes under very weak
conditions concerning the dependence structure of the process. As an
application we can prove the empirical process CLT for ergodic torus
automorphisms. Our results also apply to Markov chains and dynamical systems
having a spectral gap on some Banach space of functions. Our proof uses a
multivariate extension of the techniques introduced by Dehling, Durieu and
Voln\'y \cite{DehDurVol09} in the univariate case. As an important technical
ingredient, we prove a th moment bound for partial sums in multiple
mixing systems.Comment: to be published in Stochastic Processes and their Application
On multidimensional inequality with variable distribution mean
We compare alternative populations of individuals, who differ for many characteristics besides income, in terms of inequality. In order to achieve our aim, we extend the notion of Generalized Lorenz Preorder to a context of multivariate distributions with different marginals. Finally, we show, by using convex analysis, that some conditions, relevant in the analysis of multidimensional inequality, are equivalent to the ordering we introducedMultidimensional Inequality, Generalized Lorenz Preordering, Price-majorization
Growth of uniform infinite causal triangulations
We introduce a growth process which samples sections of uniform infinite
causal triangulations by elementary moves in which a single triangle is added.
A relation to a random walk on the integer half line is shown. This relation is
used to estimate the geodesic distance of a given triangle to the rooted
boundary in terms of the time of the growth process and to determine from this
the fractal dimension. Furthermore, convergence of the boundary process to a
diffusion process is shown leading to an interesting duality relation between
the growth process and a corresponding branching process.Comment: 27 pages, 6 figures, small changes, as publishe
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