48 research outputs found
Diagonalizing triangular matrices via orthogonal Pierce decompositions
A class of sufficient conditions is given to ensure that the sum a+b in a ring R, is equivalent to a sum x + y, which is an orthogonal Pierce decomposition. This is then used to show that a lower triangular matrix, with a regular diagonal is equivalent to its diagonal iff the matrix admits a lower triangular von Neumann inverse.Fundação para a Ciência e a Tecnologia (FCT) – Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI)
Some additive results on Drazin Inverses
In this paper, some additive results on Drazin inverse of a sum of Drazin invertible elements are derived. Some converse results are also presented.Fundação Luso Americana para o DesenvolvimentoUniversidade do Minho. Centro de Matemática (CMAT)Fundação para a Ciência e a Tecnologia (FCT
The (2,2,0) drazin inverse problem
We consider the additive Drazin problem and we study the existence of the Drazin inverse of a two by two matrix with zero (2,2) entry.This research was financed by FEDER Funds through ``Programa Operacional Factores de Competitividade - COMPETE'' and by Portuguese Funds through FCT - ``Fundação para a Ciência e a Tecnologia'', within the project PEst-C/MAT/UI0013/2011
Asymptotics for the Fredholm Determinant of the Sine Kernel on a Union of Intervals
In the bulk scaling limit of the Gaussian Unitary Ensemble of Hermitian
matrices the probability that an interval of length contains no eigenvalues
is the Fredholm determinant of the sine kernel over
this interval. A formal asymptotic expansion for the determinant as tends
to infinity was obtained by Dyson. In this paper we replace a single interval
of length by where is a union of intervals and present a proof
of the asymptotics up to second order. The logarithmic derivative with respect
to of the determinant equals a constant (expressible in terms of
hyperelliptic integrals) times , plus a bounded oscillatory function of
(zero of , periodic if , and in general expressible in terms of the
solution of a Jacobi inversion problem), plus . Also determined are the
asymptotics of the trace of the resolvent operator, which is the ratio in the
same model of the probability that the set contains exactly one eigenvalue to
the probability that it contains none. The proofs use ideas from orthogonal
polynomial theory.Comment: 24 page
Pocket Monte Carlo algorithm for classical doped dimer models
We study the correlations of classical hardcore dimer models doped with
monomers by Monte Carlo simulation. We introduce an efficient cluster
algorithm, which is applicable in any dimension, for different lattices and
arbitrary doping. We use this algorithm for the dimer model on the square
lattice, where a finite density of monomers destroys the critical confinement
of the two-monomer problem. The monomers form a two-component plasma located in
its high-temperature phase, with the Coulomb interaction screened at finite
densities. On the triangular lattice, a single pair of monomers is not
confined. The monomer correlations are extremely short-ranged and hardly change
with doping.Comment: 6 pages, REVTeX
Kosterlitz Thouless Universality in Dimer Models
Using the monomer-dimer representation of strongly coupled U(N) lattice gauge
theories with staggered fermions, we study finite temperature chiral phase
transitions in (2+1) dimensions. A new cluster algorithm allows us to compute
monomer-monomer and dimer-dimer correlations at zero monomer density (chiral
limit) accurately on large lattices. This makes it possible to show
convincingly, for the first time, that these models undergo a finite
temperature phase transition which belongs to the Kosterlitz-Thouless
universality class. We find that this universality class is unaffected even in
the large N limit. This shows that the mean field analysis often used in this
limit breaks down in the critical region.Comment: 4 pages, 4 figure
The resultant on compact Riemann surfaces
We introduce a notion of resultant of two meromorphic functions on a compact
Riemann surface and demonstrate its usefulness in several respects. For
example, we exhibit several integral formulas for the resultant, relate it to
potential theory and give explicit formulas for the algebraic dependence
between two meromorphic functions on a compact Riemann surface. As a particular
application, the exponential transform of a quadrature domain in the complex
plane is expressed in terms of the resultant of two meromorphic functions on
the Schottky double of the domain.Comment: 44 page