• Corpus ID: 250264958

Gaussian Fluctuation for Smoothed Local Correlations in CUE

  title={Gaussian Fluctuation for Smoothed Local Correlations in CUE},
  author={Alexander Soshnikov},
. Motivated by the Rudnick-Sarnak theorem we study limiting distribution of smoothed local correlations of the form for the Circular United Ensemble of random matrices for sufficiently smooth test functions. 



Central Limit Theorem for $C\beta E$ Pair Dependent Statistics in Mesoscopic Regime

We extend our results on the fluctuation of the pair counting statistic of the Circular Beta Ensemble $\sum_{i\neq j}f(L_N(\theta_i-\theta_j))$ for arbitrary $\beta>0$ in the mesoscopic regime

The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities

Author(s): Soshnikov, Alexander | Abstract: We discuss CLT for the global and local linear statistics of random matrices from classical compact groups. The main part of our proofs are certain

L-Functions and Random Matrices

In 1972 H. L. Montgomery announced a remarkable connection between the distribution of the zeros of the Riemann zeta-function and the distribution of eigenvalues of large random Hermitian matrices.

Pair dependent linear statistics for CβE

We study the limiting distribution of a pair counting statistics of the form [Formula: see text] for the circular [Formula: see text]-ensemble (C[Formula: see text]E) of random matrices for

Level spacings distribution for large random matrices: Gaussian fluctuations

We study the level-spacings distribution for eigenvalues of large N X N matrices from the classical compact groups in the scaling limit when the mean distance between nearest eigenvalues equals 1.

Pair correlation of zeros of the zeta function.

s T— »oo and U-+Q in such a way that UL = A; here L = ̂ —logT is the average 2n density of zeros up to T and A is an arbitrary positive constant. If the same number of points were distributed at

High powers of random elements of compact Lie groups

Summary.If a random unitary matrix $U$ is raised to a sufficiently high power, its eigenvalues are exactly distributed as independent, uniform phases. We prove this result, and apply it to give exact

On the eigenvalues of random matrices

Let M be a random matrix chosen from Haar measure on the unitary group Un. Let Z = X + iY be a standard complex normal random variable with X and Y independent, mean 0 and variance ½ normal

The circular unitary ensemble and the Riemann zeta function: the microscopic landscape and a new approach to ratios

We show in this paper that after proper scalings, the characteristic polynomial of a random unitary matrix converges to a random analytic function whose zeros, which are on the real line, form a

Linear functionals of eigenvalues of random matrices

Let Mn be a random n×n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear combinations of traces