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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 $β \geq 1$ . 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,...

Generalized deformed commutation relations with nonzero minimal uncertainties in position and/or momentum and applications to quantum mechanics.

Quesne, Christiane, Tkachuk, Volodymyr M. (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Generalized q-deformed Gaussian random variables

Marek Bożejko, Hiroaki Yoshida (2006)

Banach Center Publications

We produce generalized q-Gaussian random variables which have two parameters of deformation. One of them is, of course, q as for the usual q-deformation. We also investigate the corresponding Wick formulas, which will be described by some joint statistics on pair partitions.

Geometric Quantization and Multiplicities of Group Representations.

V. Guillemin, S. Sternberg (1982)

Inventiones mathematicae

Geometry of the Kepler system in coherent states approach

Maciej Horowski, Anatol Odzijewicz (1993)

Annales de l'I.H.P. Physique théorique

Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group

Benjamin Cahen (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let $G$ be a quasi-Hermitian Lie group with Lie algebra $𝔤$ and $K$ be a compactly embedded subgroup of $G$ . Let $ξ_{0}$ be a regular element of $𝔤^{*}$ which is fixed by $K$ . We give an explicit $G$ -equivariant diffeomorphism from a complex domain onto the coadjoint orbit $𝒪 (ξ_{0})$ of $ξ_{0}$ . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where $𝒪 (ξ_{0})$ is associated with a unitary irreducible representation of $G$ which is holomorphically...