We establish sharp results on the modulus of continuity distribution spectral measure for multi-frequency Schrodinger operators with Diphantine frequencies and small analytic potentials.

Broadband UV measurements are evaluated when UV-A irradiance meters measure optical radiation from 365 nm UV sources. The CIE standardized rectangular-shape UV-A function can be realized only with large spectral mismatch errors. The spectral power-distribution of the 365 nm excitation source is not standardized. Accordingly, the readings made with different types of UV meters, even if they meas...

The efficiency of spectral clustering depends heavily on the similarity measure adopted. A widely used similarity measure is the Gaussian kernel function where Euclidean distance is used. Unfortunately, the result of spectral clustering is very sensitive to the scaling parameter and the Euclidean distance is usually not suitable to the complex distribution data. In this paper, a spectral cluste...

where Y ∈ Rp×n is a rectangular p×n matrix with random centered entries, and both n and p ≤ n tend to infinity: typically p = p(n), and p(n)/n tends to some limit. M can be seen as the empirical covariance matrix of a random vector of dimension p sampled n times, each sample being a column of Y . It is common in applications to have a number of variables with a comparable order of magnitude wit...

We compute an asymptotic expansion with precision 1/n of the moments of the expected empirical spectral measure of Wigner matrices of size n with independent centered entries. We interpret this expansion as the moments of the addition of the semicircle law and 1/n times an explicit signed measured with null total mass. This signed measure depends only on the second and fourth moments of the ent...