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Determinant maximization with linear matrix inequality constraints
Matrix linear matrix inequality (lmi) computational geometry statistics system identification communication theory
2015/8/11
The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment desig...
Asymptotics of the Fredholm determinant corresponding to the first bulk critical universality class in random matrix models
Integrable operators Riemann-Hilbert approach Deift-Zhou method asymptotical analysis of Fredholm determinants
2015/1/19
We study the one-parameter family of determinants $det(I-\gamma K_{PII}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{PII}$ acting on the interval $(-s,s)$ whose kernel is constructed o...
On the asymptotics of a Toeplitz determinant with singularities
the asymptotics of a Toeplitz determinant singularities Functional Analysis
2012/6/25
We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We also relax the smoothness conditions on the re...
A determinant of generalized Fibonacci numbers
generalized Fibonacci numbers Cassini’s identity determinant evaluation
2012/4/18
We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of the...
The Fuglede-Kadison determinant, theme and variations
Determinant Fuglede-Kadison determinant Banach algebra
2011/8/25
Abstract: We review the definition of determinants for finite von Neumann algebras, due to Fuglede and Kadison (1952), and a generalisation for appropriate groups of invertible elements in Banach alge...
Stability of waves using the Fredholm determinant
Stability of waves Fredholm determinant Analysis of PDEs
2011/8/23
Abstract: We present a new method for reducing the Fredholm determinant associated with an underlying Birman-Schwinger operator to a finite dimensional determinant. Moreover, we compute explicitly the...
A New Algorithm for Determinant Evaluation - The Reduction Method
New Algorithm Determinant Evaluation - The Reduction Method
2011/1/19
We present here a new method for determinant evaluation – the reduction method. Firstly,in the section 2, we apply it to third order determinants and after, in the section 3, we generalize it to highe...
On the functional determinant of a special operator with a zero mode in cosmology
functional determinant special operator
2011/3/2
The functional determinant of a special second order quantum-mechanical operator is calcu-lated with its zero mode gauged out by the method of the Faddeev-Popov gauge fixing procedure.
Determinant line bundle on moduli space of parabolic bundles
Parabolic bundle determinant bundle Quillen metric
2011/2/24
In [BR1], [BR2], a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it.The construction of the Hermitian structure w...
Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of reflection algebra. We give a combinatoria...
Explicit Formula for the Hyperbolic Scattering Determinant
explicit formulas hyperbolic scattering determinant
2007/12/11
We prove the explicit formula for the hyperbolic scattering determinant in the case of a general subgroup $\Gamma $ of ${\rm PSL}\left( 2,\mathbb{R}\right) $. The class of test functions involved (not...