357 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
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
On Soliton-type Solutions of Equations Associated with N-component Systems
The algebraic geometric approach to -component systems of nonlinear
integrable PDE's is used to obtain and analyze explicit solutions of the
coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to
anti-kink transitions and multi-peaked soliton solutions is carried out.
Transformations are used to connect these solutions to several other equations
that model physical phenomena in fluid dynamics and nonlinear optics.Comment: 43 pages, 16 figure
Novel microwave apparatus for breast lesions detection: Preliminary clinical results
This paper presents preliminary results of an innovative microwave imaging apparatus for breast lesions detection. Specially, a Huygens Principle based method is employed to process the microwave signals and to build the respective microwave images. The apparatus has been first tested on phantoms. Next, its performance has been verified through clinical examinations on 22 healthy breasts and on 29 breast having lesions, using as gold standard the output of the radiologist study review obtained using conventional techniques. Specifically, we introduce a metric, which is the ratio between maximum and average of the image intensity (MAX/AVG). We found that MAX/AVG of microwave images can be used for classifying breasts containing lesions. In addition, using MAX/AVG as classification parameter, receiver operating characteristic curves have been empirically determined. Furthermore, for one randomly selected breast having lesion, we have demonstrated that the localisation of the inclusion acquired through microwave imaging is compatible with mammography images
Large N expansion of the 2-matrix model
We present a method, based on loop equations, to compute recursively all the
terms in the large topological expansion of the free energy for the
2-hermitian matrix model. We illustrate the method by computing the first
subleading term, i.e. the free energy of a statistical physics model on a
discretized torus.Comment: 41 pages, 9 figures eps
Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation
We consider the problem of describing the possible spectra of an acoustic
operator with a periodic finite-gap density. We construct flows on the moduli
space of algebraic Riemann surfaces that preserve the periods of the
corresponding operator. By a suitable extension of the phase space, these
equations can be written with quadratic irrationalities.Comment: 15 page
Wannier functions for quasi-periodic finite-gap potentials
In this paper we consider Wannier functions of quasi-periodic g-gap () potentials and investigate their main properties. In particular, we discuss
the problem of averaging underlying the definition of Wannier functions for
both periodic and quasi-periodic potentials and express Bloch functions and
quasi-momenta in terms of hyperelliptic functions. Using this approach
we derive a power series expansion of the Wannier function for quasi-periodic
potentials valid at and an asymptotic expansion valid at large
distance. These functions are important for a number of applied problems
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