Related papers: Coupling of eigenvalues of complex matrices at dia…
A coupling method is developed for univariate extreme value theory , providing an alternative to the use of the tail empirical/quantile processes. Emphasizing the Peak-over-Threshold approach that approximates the distribution above high…
This paper formulates a notion of high-dimensional random dynamical systems that couple to another system, like an embedding environment, in such a way that each system engages in controlled exchange with the other system. Using the…
We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multiple. We provide analyticity results for the dependence of…
It is well known that the Poisson-Boltzmann (PB) equation yields the exact counterion density around charged objects in the weak coupling limit. In this paper we generalize the PB approach to account for coupling of arbitrary strength by…
For given k distinct complex conjugate pairs, l distinct real numbers, and a given graph G on 2k+l vertices with a matching of size at least k, we will show that there is a real matrix whose eigenvalues are the given numbers and its graph…
In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…
The concept of exceptional point (EP) is demonstrated experimentally in the case of a simple mechanical system consisting of two linearized coupled pendulums. Exceptional points correspond to specific values of the system parameters that…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
We consider the trace map associated with the Fibonacci Hamiltonian as a diffeomorphism on the invariant surface associated with a given coupling constant and prove that the non-wandering set of this map is hyperbolic if the coupling is…
For a real or complex one-dimensional map satisfying a weak hyperbolicity assumption, we study the existence and statistical properties of physical measures, with respect to geometric reference measures. We also study geometric properties…
We develop a strong coupling approach for a general lattice problem. We argue that this strong coupling perspective represents the natural framework for a generalization of the dynamical mean field theory (DMFT). The main result of this…
We investigate the joint convergence of independent random Toeplitz matrices with complex input entries that have a pair-correlation structure, along with deterministic Toeplitz matrices and the backward identity permutation matrix.…
A complete definition of the cycles, on the auxiliary Riemann surface defined by Martinec and Warner for describing pure N=2 gauge theories with arbitrary group, is provided. The strong coupling monodromies around the vanishing cycles are…
We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small off-diagonal elements…
We show that for many complex parameters a, the set of points that converge to infinity under iteration of the exponential map f(z)=e^z+a is connected. This includes all parameters for which the singular value escapes to infinity under…
There is recent interest in the inter and intra element interactions of metamaterial unit cells. To calculate the effects of these interactions which can be substantial, an ab initio general coupled mode equation, in the form of an…
Present laboratory limits on the coupling strength of anomalous pseudoscalar and axial interactions are many orders of magnitude weaker than their scalar and vector analogs. Here we investigate two mechanisms which can circumvent this…
A method is described for the extrapolation of perturbative expansions in powers of asymptotically small coupling parameters or other variables onto the region of finite variables and even to the variables tending to infinity. The method…
The variety of the phase transitions in Induced QCD are studied. Depending upon the parameters in the scalar field potential, there could be infinite number of fixed points, with different critical behavior. The integral equation for the…
In many--body and other systems, the physics situation often allows one to interpret certain, distinct states by means of a simple picture. In this interpretation, the distinct states are not eigenstates of the full Hamiltonian. Hence,…