共查询到20条相似文献,搜索用时 0 毫秒
1.
Alexander Soshnikov 《Journal of statistical physics》2003,113(3-4):611-622
We extend the main result of the companion paper J. Stat. Phys.
113:595–610 to the case of the pfaffian ensembles. 相似文献
2.
M. Shcherbina 《Journal of statistical physics》2009,136(1):35-50
We prove edge universality of local eigenvalue statistics for orthogonal invariant matrix models with real analytic potentials
and one interval limiting spectrum. Our starting point is the result of Shcherbina (Commun. Math. Phys. 285, 957–974, 2009) on the representation of the reproducing matrix kernels of orthogonal ensembles in terms of scalar reproducing kernel of
corresponding unitary ensemble. 相似文献
3.
We review the algebraic structures imposed on the renormalization procedure in terms of Hopf and Lie algebras of Feynman graphs, and exhibit the connection to diffeomorphisms of physical observables. 相似文献
4.
We show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved Bernoulli measures , for the golden mean. In this first part we establish some large-deviation results for random products of matrices, using perturbation theory of quasicompact operators. 相似文献
5.
Correlations for parameter-dependent Gaussian random matrices, intermediate between symmetric and Hermitian and antisymmetric
Hermitian and Hermitian, are calculated. The (dynamical) density-density correlation between eigenvalues at different values
of the parameter is calculated for the symmetric to Hermitian transition and the scaledN→∞ limit is computed. For the antisymmetric Hermitian to Hermitian transition the equal-parametern-point distribution function is calculated and the scaled limit computed. A circular version of the antisymmetric Hermitian
to Hermitian transition is formulated. In the thermodynamic limit the equal-parameter distribution function is shown to coincide
with the scaled-limit expression of this distribution for the Gaussian antisymmetric Hermitian to Hermitian transition. Furthermore,
the thermodynamic limit of the corresponding density-density correlation is computed. The results for the correlations are
illustrated by comparison with empirical correlations calculated from numerical data obtained from computer-generated Gaussian
random matrices. 相似文献
6.
The problem of colliding gravitational waves gives rise to a Goursat problem in the triangular region 1 x < y 1 for a certain 2 × 2 matrix valued nonlinear equation. This equation, which is a particular exact reduction of the vacuum Einstein equations, is integrable, i.e. it possesses a Lax pair formulation. Using the simultaneous spectral analysis of this Lax pair we study the above Goursat problem as well as its linearized version. It is shown that the linear problem reduces to a scalar Riemann–Hilbert problem, which can be solved in closed form, while the nonlinear problem reduces to a 2 × 2 matrix Riemann–Hilbert problem, which under certain conditions is solvable. 相似文献
7.
E. Ryckman 《Journal of statistical physics》2008,132(3):473-486
For arbitrary β>0, we use the orthogonal polynomials techniques developed in (Killip and Nenciu in , 2005; Killip and Nenciu in Int. Math. Res. Not. 50: 2665–2701, 2004) to study certain linear statistics associated with the circular and Jacobi β ensembles. We identify the distribution of these statistics then prove a joint central limit theorem. In the circular case,
similar statements have been proved using different methods by a number of authors. In the Jacobi case these results are new. 相似文献
8.
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg–de Vries equation for
decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this
method.
Research supported by the Austrian Science Fund (FWF) under grant no. Y330. 相似文献
9.
For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann–Hilbert problem approach is used to derive the leading-order asymptotics as
of solutions
to the Cauchy problem for the defocusing nonlinear Schrödinger equation (
NLSE),
, with finite-density initial data
.The
NLSE dark soliton position shifts in the presence of the continuum are also obtained. 相似文献
10.
11.
In this work, we develop an orthogonal-polynomials approach for random matrices with orthogonal or symplectic invariant laws, called one-matrix models with polynomial potential in theoretical physics, which are a generalization of Gaussian random matrices. The representation of the correlation functions in these matrix models, via the technique of quaternion determinants, makes use of matrix kernels. We get new formulas for matrix kernels, generalizing the known formulas for Gaussian random matrices, which essentially express them in terms of the reproducing kernel of the theory of orthogonal polynomials. Finally, these formulas allow us to prove the universality of the local statistics of eigenvalues, both in the bulk and at the edge of the spectrum, for matrix models with two-band quartic potential by using the asymptotics given by Bleher and Its for the corresponding orthogonal polynomials. 相似文献
12.
It is shown that response properties of a quantum harmonic oscillator are in essence those of a classical oscillator, and that, paradoxical as it may be, these classical properties underlie all quantum dynamical properties of the system. The results are extended to noninteracting bosonic fields, both neutral and charged. 相似文献
13.
Horst–Heino V. Borzeszkowski Hans–Jürgen Treder 《General Relativity and Gravitation》2001,33(8):1351-1369
The purely affine theory of gravity possesses a canonical formulation. For this and other reasons, it could be a promising candidate for quantum gravity. Motivated by these perspectives, we discuss spinorial matter coupled to gravity, where the latter is described by a connection having no a priori relation to a metric. We show that one can establish a truncated spinor formalism which, for special or approximate solutions to the gravitational equations, reduces to the standard formalism. As a consequence, one arrives at "matter-induced" Riemann–Cartan spaces solving the Weyl-Cartan space problem. 相似文献
14.
We show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved Bernoulli measures for the golden mean. In this second part we show how the Hausdorff dimension of the set where the measure has a power law singularity of strength is related to the large-deviation function given in Part I. 相似文献
15.
This paper is devoted to the rigorous proof of the universality conjecture of random matrix theory, according to which the limiting eigenvalue statistics ofn×n random matrices within spectral intervals ofO(n
–1) is determined by the type of matrix (real symmetric, Hermitian, or quaternion real) and by the density of states. We prove this conjecture for a certain class of the Hermitian matrix ensembles that arise in the quantum field theory and have the unitary invariant distribution defined by a certain function (the potential in the quantum field theory) satisfying some regularity conditions. 相似文献
16.
17.
Franz Merkl 《Mathematical Physics, Analysis and Geometry》1999,2(3):245-278
This article describes the solution of the Kadomcev–Petviashvilli equation with C10 real periodic initial data in terms of an asymptotic expansion of Bloch functions. The Bloch functions are parametrized by the spectral variety of a heat equation (heat curves) with an external potential. The mentioned spectral variety is a Riemann surface of in general infinite genus; the Kadomcev–Petviashvilli flow is represented by a one-parameter-subgroup in the real part of the Jacobi variety of this Riemann surface. It is shown that the KP-I flow with these initial data propagates almost periodically. 相似文献
18.
We study the chromatic polynomials (= zero-temperature antiferromagnetic Potts-model partition functions) P
G
(q) for m×n rectangular subsets of the square lattice, with m8 (free or periodic transverse boundary conditions) and n arbitrary (free longitudinal boundary conditions), using a transfer matrix in the Fortuin–Kasteleyn representation. In particular, we extract the limiting curves of partition-function zeros when n, which arise from the crossing in modulus of dominant eigenvalues (Beraha–Kahane–Weiss theorem). We also provide evidence that the Beraha numbers B
2,B
3,B
4,B
5 are limiting points of partition-function zeros as n whenever the strip width m is 7 (periodic transverse b.c.) or 8 (free transverse b.c.). Along the way, we prove that a noninteger Beraha number (except perhaps B
10) cannot be a chromatic root of any graph. 相似文献
19.
In this Letter we introduce the (n+2)-dimensional Born–Infeld action with a dual field strength
. We compute the field equation by using Schur polynomials and give a soliton solution. 相似文献
20.
In a series of papers, we investigate the reformulation of Epstein–Glaser renormalization in coordinate space, both in analytic and (Hopf) algebraic terms. This first article deals with analytical aspects. Some of the (historically good) reasons for the divorces of the Epstein–Glaser method, both from mainstream quantum field theory and the mathematical literature on distributions, are made plain; and overcome. 相似文献