Real roots of Random Polynomials: Universality close to accumulation points

We identify the scaling region of a width O(n^{-1}) in the vicinity of the accumulation points $t=\pm 1$ of the real roots of a random Kac-like polynomial of large degree n. We argue that the density of the real roots in this region tends to a universal form shared by all polynomials with independent, identically distributed coefficients c_i, as long as the second moment \sigma=E(c_i^2) is finite. In particular, we reveal a gradual (in contrast to the previously reported abrupt) and quite nontrivial suppression of the number of real roots for coefficients with a nonzero mean value \mu_n = E(c_i) scaled as \mu_n\sim n^{-1/2}.Comment: Some minor mistakes that crept through into publication have been removed. 10 pages, 12 eps figures. This version contains all updates, clearer pictures and some more thorough explanation

Random Matrices close to Hermitian or unitary: overview of methods and results

The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical contexts, most importantly in random matrix description of quantum chaotic scattering as well as in the context of QCD-inspired random matrix models.Comment: Published version, with a few more misprints correcte

A Nuclear Jet at Chernobyl Around 21:23:45 UTC on April 25, 1986

The nature of two explosions that were witnessed within 3 s at the Chernobyl-4 reactor less than a minute after 21:23:00 UTC on April 25, 1986, have since then been the subject of sprawling interpretations. This paper renders the following hypothesis. The first explosion consisted of thermal neutron mediated nuclear explosions in one or rather a few fuel channels, which caused a jet of debris that reached an altitude of some 2500 to 3000 m. The second explosion would then have been the steam explosion most experts believe was the first one. The solid support for this new scenario rests on two pillars and three pieces of corroborating evidence. The first pillar is that a group at the V. G. Khlopin Radium Institute in then Leningrad on April 29, 1986, detected newly produced, or fresh, xenon fission products at Cherepovets, 370 km north of Moscow and far away from the major track of Chernobyl debris ejected by the steam explosion and subsequent fires. The second pillar is built on state-of-the-art meteorological dispersion calculations, which show that the fresh xenon signature observed at Cherepovets was only possible if the injection altitude of the fresh debris was considerably higher than that of the bulk reactor core releases that turned toward Scandinavia and central Europe. These two strong pieces of evidence are corroborated by what were manifest physical effects of a downward jet in the southeastern part of the reactor, by seismic measurements some 100 km west of the reactor, and by observations of a blue flash above the reactor a few seconds after the first explosion