Typical large unitary matrices show remarkable patterns in their eigenvalue distribution.
These same patterns appear in telephone encryption, the zeros of Riemann's zeta function …

We present a descriptive review of physical problems dealing with extreme values in several
fields of physics. We consider different physical situations involving random variables that …

We study the characteristic polynomials Z (U, θ) of matrices U in the Circular Unitary
Ensemble (CUE) of Random Matrix Theory. Exact expressions for any matrix size N are …

Random matrix theory is a wide and growing field with a variety of concepts, results, and
techniques and a vast range of applications in mathematics and the related sciences. The …

L-functions are important objects in modern number theory. They are generating functions
formed out of local data associated with either an arithmetic object or with an automorphic …

Let $ M_n $ be a random $ n\times n $ unitary matrix with distribution given by Haar
measure on the unitary group. Using explicit moment calculations, a general criterion is …

Linear statistics of eigenvalues in many familiar classes of random matrices are known to
obey gaussian central limit theorems. The proofs of such results are usually rather difficult …

We argue that the freezing transition scenario, previously conjectured to occur in the
statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the …

It was recently conjectured by Fyodorov, Hiary and Keating that the maximum of the
characteristic polynomial on the unit circle of a N * NN× N random unitary matrix sampled …

We argue that the freezing transition scenario, previously explored in the statistical
mechanics of 1/f—noise random energy models, also determines the value distribution of …