Brascamp–Lieb-type, weighted Poincaré-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general κ-concave probability measures (in the hierarchy of convex measures). In analogy with the limiting (infinitedimensional log-concave) Gaussian model, the weighted inequalities fully describe the measure concentration and large deviation properties of...

To quantify heavy-tailed distributions observed in financial time series, we propose a general method to characterize symmetric non-Gaussian distributions. In our approach, an observed time series is assumed to be described by the multiplication of Gaussian and amplitude random variables, where the amplitude variable describes fluctuations of the standard deviation. Based on this framework, it ...

For any hyperbolic rational map and any net of Borel probability measures on the space of Borel probability measures on the Julia set, we show that this net satisfies a strong form of the large deviation principle with a rate function given by the entropy map if and only if the large deviation and the pressure functionals coincide. To each such principles corresponds a new expression for the en...

background: the classical supportive therapy for î² -thalassemia major consists of regular blood transfusion, iron-chelation therapy and specific treatment of the related complications. a balance between the maintenance of the highest possible level of haemoglobin and lowest possible level of iron accumulation in heart and liver give the best chance of survival and the best quality of life. met...

A method was devised for combining experimental partition coefficients measured at different temperatures into a single regression correlation. The proposed method described the 265 experimental air-to-polyurethane ether adsorption coefficients reported by Kamprad and Goss (Kamprad, I.; Goss, K.-U. Anal. Chem. 2007, 79, 4222-4227) to within a standard deviation of 0.084 log units, which is comp...

Abstract. We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n/ log n can be coded by about H × n bits, where H is an explicitly...

Let Col n denote the set of all `-colored graphs on n vertices and let G be a graph drawn uniformly at random from this set. Provided that `→∞, we prove that all color classes of G deviate roughly at most √ 2 log ` from ⌊ n ` ⌋ , and there is at least one color class with such deviation. Furthermore, we prove similar results for the class Col n,M , which contains all `-colored graphs with preci...