490 research outputs found
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
-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
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