相关论文: Normal matrix models, dbar-problem, and orthogonal…
In this paper we give the asymptotic behavior of type I multiple orthogonal polynomials for a Nikishin system of order two with two disjoint intervals. We use the Riemann-Hilbert problem for multiple orthogonal polynomials and the steepest…
A class of recently introduced su(n) `free-fermion' models has recently been used to construct generalized Hubbard models. I derive an algebra defining the `free-fermion' models and give new classes of solutions. I then introduce a…
This paper explores multiple closely related themes: bounding the complexity of Diophantine equations over the integers and developing mathematical proofs in parallel with formal theorem provers. Hilbert's Tenth Problem (H10) asks about the…
We obtain the strong asymptotics of polynomials $p_n(\lambda)$, $\lambda\in\mathbb{C}$, orthogonal with respect to measures in the complex plane of the form $$ e^{-N(|\lambda|^{2s}-t\lambda^s-\overline{t\lambda}^s)}dA(\lambda), $$ where $s$…
A biorthonormal-block density-matrix renormalization group algorithm is proposed to accurately compute properties of large-scale non-Hermitian many-body systems, in which a renormalized-space partition of the non-Hermitian reduced density…
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…
A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…
We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point purely in terms of the original Hamiltonian, avoiding the normalization procedure.…
In this paper, we define a Dolbeault complex with weights according to normal crossings, which is a useful tool for studying the d-bar-equation on singular complex spaces by resolution of singularities (where normal crossings appear…
Generalizations of the Hermite polynomials to many variables and/or to the complex domain have been located in mathematical and physical literature for some decades. Polynomials traditionally called complex Hermite ones are mostly…
This paper is a continuation of our previous work in which we studied a sl(3) Zakharov-Shabat type auxiliary linear problem with reductions of Mikhailov type and the integrable hierarchy of nonlinear evolution equations associated with it.…
We construct a previously unknown $E_2$-quasi-exactly solvable non-Hermitian model whose eigenfunctions involve weakly orthogonal polynomials obeying three-term recurrence relations that factorize beyond the quantization level. The model…
Let G be a bounded Jordan domain in the complex plane and consider the infinite upper Hessenberg matrix M associated with the Bergman orthogonal polynomials of G. This matrix represents the Bergman shift operator of G. The main purpose of…
We present a new closed form for the interpolating polynomial of the general univariate Hermite interpolation that requires only calculation of polynomial derivatives, instead of derivatives of rational functions. This result is used to…
We study the basic features of the two-dimensional quantum Hubbard Model at half-filling by means of the L\"uscher algorithm and the algorithm based on direct update of the determinant of the fermionic matrix. We implement the L\"uscher…
This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal $I$. The criterion used in the computation involves specific commutation polynomials and leads to an algorithm and an implementation extending…
The Hermite-Gaussian (HG) modes make up a complete and orthonormal basis, which have been extensively used to describe optical fields. Here, we demonstrate, for the first time to our knowledge, deep learning-based modal decomposition (MD)…
One of effective ways to solve the equivalence problem and describe moduli spaces for real submanifolds in complex space is the normal form approach. In this survey, we outline some normal form constructions in CR-geometry and formulate a…
These lectures introduce the method of nonlinear steepest descent for Riemann-Hilbert problems. This method finds use in studying asymptotics associated to a variety of special functions such as the Painlev\'{e} equations and orthogonal…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…