Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques, and applications to graphical enumeration

We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal polynomials. We obtain the first proof of a complete large N expansion for the partition function, for a general class of probability measures on matrices, originally conjectured by Bessis, Itzykson, and Zuber. We prove that the coefficients in the asymptotic expansion are analytic functions of parameters in the original probability measure, and that they are generating functions for the enumeration of labelled maps according to genus and valence. Central to the analysis is a large N expansion for the mean density of eigenvalues, uniformly valid on the entire real axis.Comment: 44 pages, 4 figures. To appear, International Mathematics Research Notice

Anomalous magnetotransport and cyclotron resonance of high mobility magnetic 2DHGs in the quantum Hall regime

Low temperature magnetotransport measurements and far infrared transmission spectroscopy are reported in molecular beam epitaxial grown two-dimensional hole systems confined in strained InAs quantum wells with magnetic impurities in the channel. The interactions of the free holes spin with the magnetic moment of 5/2 provided by manganese features intriguing localization phenomena and anomalies in the Hall and the quantum Hall resistance. In magnetic field dependent far infrared spectroscopy measurements well pronounced cyclotron resonance and an additional resonance are found that indicates an anticrossing with the cyclotron resonance

Iso-spectral deformations of general matrix and their reductions on Lie algebras

We study an iso-spectral deformation of general matrix which is a natural generalization of the Toda lattice equation. We prove the integrability of the deformation, and give an explicit formula for the solution to the initial value problem. The formula is obtained by generalizing the orthogonalization procedure of Szeg\"{o}. Based on the root spaces for simple Lie algebras, we consider several reductions of the hierarchy. These include not only the integrable systems studied by Bogoyavlensky and Kostant, but also their generalizations which were not known to be integrable before. The behaviors of the solutions are also studied. Generically, there are two types of solutions, having either sorting property or blowing up to infinity in finite time.Comment: 25 pages, AMSLaTe

A heterotrimeric G protein, G alpha i-3, on Golgi membranes regulates the secretion of a heparan sulfate proteoglycan in LLC-PK1 epithelial cells

A heterotrimeric G-alpha-i subunit, alpha-i-3, is localized on Golgi membranes in LLC-PK1 and NRK epithelial cells where it colocalizes with mannosidase II by immunofluorescence. The alpha-i-3 was found to be localized on the cytoplasmic face of Golgi cisternae and it was distributed across the whole Golgi stack. The alpha-i-3 subunit is found on isolated rat liver Golgi membranes by Western blotting and G-alpha-i-3 on the Golgi apparatus is ADP ribosylated by pertussis toxin. LLC-PK1 cells were stably transfected with G-alpha-i-3 on an MT-1, inducible promoter in order to overexpress alpha-i-3 on Golgi membranes. The intracellular processing and constitutive secretion of the basement membrane heparan sulfate proteoglycan (HSPG) was measured in LLC-PK1 cells. Overexpression of alpha-i-3 on Golgi membranes in transfected cells retarded the secretion of HSPG and accumulated precursors in the medial-trans-Golgi. This effect was reversed by treatment of cells with pertussis toxin which results in ADP-ribosylation and functional uncoupling of G-alpha-i-3 on Golgi membranes. These results provide evidence for a novel role for the pertussis toxin sensitive G-alpha-i-3 protein in Golgi trafficking of a constitutively secreted protein in epithelial cells

Topological Phenomena in the Real Periodic Sine-Gordon Theory

The set of real finite-gap Sine-Gordon solutions corresponding to a fixed spectral curve consists of several connected components. A simple explicit description of these components obtained by the authors recently is used to study the consequences of this property. In particular this description allows to calculate the topological charge of solutions (the averaging of the $x$-derivative of the potential) and to show that the averaging of other standard conservation laws is the same for all components.Comment: LaTeX, 18 pages, 3 figure

Large-N expansion for the time-delay matrix of ballistic chaotic cavities

We consider the 1/N-expansion of the moments of the proper delay times for a ballistic chaotic cavity supporting N scattering channels. In the random matrix approach, these moments correspond to traces of negative powers of Wishart matrices. For systems with and without broken time reversal symmetry (Dyson indices β=1 and β=2) we obtain a recursion relation, which efficiently generates the coefficients of the 1/N-expansion of the moments. The integrality of these coefficients and their possible diagrammatic interpretation is discussed