Related papers: A periodic hexagon tiling model and non-Hermitian …
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous…
Polymer blends offer an exciting material for various potential applications due to their tunable properties by varying constituting components and their relative composition. Our simulation results unravel an intrinsic relationship between…
We use the steepest descents method to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P_{N}(z_{1},...,z_{N}) = Z_{N}^{-1} e^{-N\Sigma_{i=1}^{N}V_{\alpha}(z_{i})}…
In this paper, we consider the large time asymptotic behavior of solutions to systems of two cubic nonlinear Schr"odinger equations in one space dimension. It turns out that for a system there exists a small solution of which asymptotic…
We consider a general Hermitian holomorphic line bundle $L$ on a compact complex manifold $M$ and let ${\Box}^q_p$ be the Kodaira Laplacian on $(0,q)$ forms with values in $L^p$. The main result is a complete asymptotic expansion for the…
We study the normal matrix model, also known as the two-dimensional one-component plasma at a specific temperature, with merging singularity. As the number $n$ of particles tends to infinity we obtain the limiting local correlation kernel…
We consider a non-Hermitian matrix orthogonality on a contour in the complex plane. Given a diagonalizable and rational matrix valued weight, we show that the Christoffel--Darboux (CD) kernel, which is built in terms of matrix orthogonal…
We analyse the dynamics of a two dimensional system of interacting active dumbbells. We characterise the mean-square displacement, linear response function and deviation from the equilibrium fluctuation-dissipation theorem as a function of…
A thin two-layered waveguide is considered. The governing equations for this waveguide is a matrix Klein--Gordon equation of dimension~2. A formal solution of this system in the form of a double integral can be obtained by using Fourier…
We study the influence of quenched disorder on the two-dimensional melting behavior by using both video-microscopy of superparamagnetic colloidal particles and computer simulations of repulsive parallel dipoles. Quenched disorder is…
In this paper, we consider one--parameter ($\lambda>0$) families of Li\'enard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of $\lambda>0$. To prove our…
We analyze domino tilings of the two-periodic Aztec diamond by means of matrix valued orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non-intersecting path model with periodic transition matrices. In a…
We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as model for the low-temperature vibrational properties of glass. Exact…
We present an asymptotically exact solution of a paradigmatic non-Hermitian model: the disordered interacting fermionic Hatano-Nelson model, or equivalently, the non-Hermitian spin-1/2 XXZ model. We use a renormalization group method suited…
We study double integral representations of Christoffel-Darboux kernels associated with two examples of Hermite-type matrix orthogonal polynomials. We show that the Fredholm determinants connected with these kernels are related through the…
The aim of this note is twofold. The first one is to find conditions on the asymptotic sequence which ensures differentiation of a general asymptotic expansion with respect to it. Our method results from the classical one but generalizes…
Three-dimensional integer partitions provide a convenient representation of codimension-one three-dimensional random rhombus tilings. Calculating the entropy for such a model is a notoriously difficult problem. We apply transition matrix…
We study whether in the setting of the Deift-Zhou nonlinear steepest descent method one can avoid solving local parametrix problems explicitly, while still obtaining asymptotic results. We show that this can be done, provided an a priori…
We consider a non-uniformly elliptic second-order differential operator with periodic coefficients that models composite media consisting of highly anisotropic cylindrical fibres periodically distributed in an isotropic background. The…