This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example, which needs to be investigated first, the main bounds are extended to families of Hermitian Wigner matrices by means of the Tao and Vu Four Moment Theorem and re...

We consider N ×N Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance N for some positive β > 0. We prove that the local eigenvalue statistics follows the universal Dyson sine kernel. AMS Subject Classification: 15A52, 82B44 Running title: Universality for Wigner matrices

It is proposed to use time-frequency analysis of vocal fold's onset signal for diagnosis of different phonation disorders evoked by pathological changes. The vibration signals are acquired by direct optical inspection of the glottis using an endoscope and a high speed CCD camera system. Because of their outstanding performance the Wigner distribution is used as an analysis tool. It is shown tha...

Recently, it was shown that information conveyed by the discrete Wigner distribution is highly redundant, linear relations connecting its time-frequency components. This means that every component of the discrete Wigner distribution can be expressed as a linear combination of the elements of a basis. This set of generators consists of particular time-frequency components of the distribution. Ho...

The propagation of mutual intensity through quadratic graded-index media or free space can be expressed in terms of two-dimensional fractional Fourier transforms for one-dimensional systems and in terms of fourdimensional fractional Fourier transforms for two-dimensional systems. As light propagates, its mutual intensity distribution is continually fractional Fourier transformed. These results ...

The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction. Models can be decomposed in two components corresponding to large scale and small scale variations. In practice, the large scale velocity model component can be estimated with high accuracy using repeated migration/tomography cycles, but the small scale component cannot. When ...