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Multi-variate correlation and mixtures of product measures

Tim Austin (2020)

Kybernetika

Total correlation (‘TC’) and dual total correlation (‘DTC’) are two classical ways to quantify the correlation among an n -tuple of random variables. They both reduce to mutual information when n = 2 . The first part of this paper sets up the theory of TC and DTC for general random variables, not necessarily finite-valued. This generality has not been exposed in the literature before. The second part considers the structural implications when a joint distribution μ has small TC or DTC. If TC ( μ ) = o ( n ) , then μ is...

On continuous collections of measures

Robert M. Blumenthal, Harry H. Corson (1970)

Annales de l'institut Fourier

An integral representation theorem is proved. Each continuous function from a totally disconnected compact space M to the probability measures on a complete metric space X is shown to be the resolvent of a probability measure on the space of continuous functions from M to X .

On d-finite tuples in random variable structures

Shichang Song (2013)

Fundamenta Mathematicae

We prove that the d-finite tuples in models of ARV are precisely the discrete random variables. Then, we apply d-finite tuples to the work by Keisler, Hoover, Fajardo, and Sun concerning saturated probability spaces. In particular, we strengthen a result in Keisler and Sun's recent paper.

On elliptic curves and random matrix theory

Mark Watkins (2008)

Journal de Théorie des Nombres de Bordeaux

Rubinstein has produced a substantial amount of data about the even parity quadratic twists of various elliptic curves, and compared the results to predictions from random matrix theory. We use the method of Heegner points to obtain a comparable (yet smaller) amount of data for the case of odd parity. We again see that at least one of the principal predictions of random matrix theory is well-evidenced by the data.

On some contributions to quantum structures by fuzzy sets

Beloslav Riečan (2007)

Kybernetika

It is well known that the fuzzy sets theory can be successfully used in quantum models ([5, 26]). In this paper we give first a review of recent development in the probability theory on tribes and their generalizations – multivalued (MV)-algebras. Secondly we show some applications of the described method to develop probability theory on IF-events.

On the distribution of random variables corresponding to Musielak-Orlicz norms

David Alonso-Gutiérrez, Sören Christensen, Markus Passenbrunner, Joscha Prochno (2013)

Studia Mathematica

Given a normalized Orlicz function M we provide an easy formula for a distribution such that, if X is a random variable distributed accordingly and X₁,...,Xₙ are independent copies of X, then 1 / C p | | x | | M | | ( x i X i ) i = 1 | | p C p | | x | | M , where C p is a positive constant depending only on p. In case p = 2 we need the function t ↦ tM’(t) - M(t) to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into L₁[0,1]. We also provide a general result replacing the p -norm by an arbitrary N-norm. This...

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