We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ∼ N . All previous results concerning universality of non-Gaussian random matrices are for meanfield models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique e...

The theory of period doublings for one-parameter families of iterated real mappings is generalized to period n-tuplings for complex mappings. An n-tupling occurs when the eigenvalue of a stable periodic orbit passes through the value ω = exp(2τπm/n) as the parameter value is changed. Each choice of m defines a different sequence of rc-tuplings, for which we construct a period ft-tupling renorma...

We extend the notion of universality of a function, due to Turing, to arbitrary (countable) effective domains, taking care to disallow any cheating on the part of the representations used. Then, we can be certain that effective universal functions cannot simulate non-effective functions.

We perform a systematic study of several models that have been proposed for the purpose of understanding the motion of driven interfaces in disordered media. We identify two distinct universality classes. (i) One of these, referred to as directed percolation depinning (DPD), can be described by a Langevin equation similar to the Kardar-Parisi-Zhang equation, but with quenched disorder. (ii) The...

Firstly, we prove a functional relation for the Tornheim double zeta function. Using this functional relation, we obtain simple proofs of some known formulas for special values of Tornheim and Euler-Zagier double zeta functions. Secondly, we obtain functional relations for Witten zeta functions by using a double L-values relation. By these functional relations, we obtain new proofs of known res...

We introduce here a new universality conjecture for levels of random Hamiltonians, in the same spirit as the local REM conjecture made by S. Mertens and H. Bauke. We establish our conjecture for a wide class of Gaussian and non-Gaussian Hamiltonians, which include the p-spin models, the Sherrington-Kirkpatrick model and the number partitioning problem. We prove that our universality result is o...

The supersymmetric one-loop contribution to the quark-lepton universality violation in the low-energy charged current weak interactions is studied. It is shown that the recent experimental data with the 1-σ deviation from the universality may be explained by the existence of the light sleptons (< 220GeV) and relatively light chargino and neutralinos (< 600GeV) with significant gaugino component...

We establish asymptotics for Christoffel functions, and universality limits, associated with multivariate orthogonal polynomials, on the boundary of the unit ball in Rd. Orthogonal Polynomials, Universality Limits, Christoffel functions. 42C05, 42C99, 42B05, 60B20