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Gap universality of generalized Wigner and β -ensembles

László Erdős, Horng-Tzer Yau (2015)

Journal of the European Mathematical Society

We consider generalized Wigner ensembles and general β -ensembles with analytic potentials for any β ≥ 1 . The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian β -ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact,...

Generalización del teorema de Hanson y Russo para B-variables aleatorias.

Víctor Hernández, Juan J. Romo (1986)

Trabajos de Estadística

En este trabajo se presenta una generalización de un teorema de D. L. Hanson y R. P. Russo (1981) para variables aleatorias i.i.d. que toman valores en un espacio de Banach separable (B-variables), en el esquema más general de la ley de Marcinkiewicz y Zygmund.Imponiendo condiciones sobre los momentos y el tipo Rademacher del espacio se obtienen resultados de la formamáx(np/α≤j≤n) j-1/p ||Sn - Sn-j|| → 0, casi seguro, cuando n → ∞

Generalized versions of MV-algebraic central limit theorems

Piotr Nowak, Olgierd Hryniewicz (2015)

Kybernetika

MV-algebras can be treated as non-commutative generalizations of boolean algebras. The probability theory of MV-algebras was developed as a generalization of the boolean algebraic probability theory. For both theories the notions of state and observable were introduced by abstracting the properties of the Kolmogorov's probability measure and the classical random variable. Similarly, as in the case of the classical Kolmogorov's probability, the notion of independence is considered. In the framework...

Green functions on self-similar graphs and bounds for the spectrum of the laplacian

Bernhard Krön (2002)

Annales de l’institut Fourier

Combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis we introduce a new method for spectral analysis on self-similar graphs.First, for a rather general, axiomatically defined class of self-similar graphs a graph theoretic analogue to the Banach fixed point theorem is proved. The subsequent results hold for a subclass consisting of “symmetrically” self-similar graphs which however is still more general then...

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