相关论文: Orthogonal Polynomials and Fluctuations of Random …
In this article, we study relations between the local geometry of planar graphs (combinatorial curvature) and em global geometric invariants, namely the Cheeger constants and the exponential growth. We also discuss spectral applications.
Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point…
We show that the linear strands of the Tor of determinantal varieties in spaces of symmetric and skew-symmetric matrices are irreducible representations for the periplectic (strange) Lie superalgebra. The structure of these linear strands…
We argue that an ensemble of backgrounds best understands hydrodynamic dispersion relations in a medium with few degrees of freedom and is therefore subject to strong thermal fluctuations. In the linearized regime, dispersion relations…
The Landau--Lifshitz--Gilbert equations for the evolution of the magnetization, in presence of an external torque, can be cast in the form of the Lorenz equations and, thus, can describe chaotic fluctuations. To study quantum effects, we…
A generalization of the Lorenz equations is proposed where the variables take values in a Lie algebra. The finite dimensionality of the representation encodes the quantum fluctuations, while the non-linear nature of the equations can…
In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in…
We consider global fluctuations of the spectrum of the GUE. Using results on the linear statistics of such matrices as well as variance bounds on the eigenvalues, we show that under a suitable scaling, global fluctuations of the spectrum…
We prove a determinantal formula for quantities related to the problem of enumeration of (semi-) meanders, namely the topologically inequivalent planar configurations of non-self-intersecting loops crossing a given (half-) line through a…
Fluctuation theorems establish deep relations between observables away from thermal equilibrium. Until recently, the research on fluctuation theorems was focused on time-reversal-invariant systems. In this review we address some newly…
We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several properties that have been out of reach before: generating…
Most astrophysical fluids are turbulent and magnetized. Fluctuations of polarization provide a promising way to study astrophysical magnetic turbulence. We discuss polarization that arises from grains and atoms aligned in respect to…
Analytic expressions for the Fourier transforms of the Chebyshev and Legendre polynomials are derived, and the latter is used to find a new representation for the half-order Bessel functions. The numerical implementation of the so-called…
We consider extremal eigenvalues of sparse random matrices, a class of random matrices including the adjacency matrices of Erd\H{o}s-R\'{e}nyi graphs $\mathcal{G}(N,p)$. Recently, it was shown that the leading order fluctuations of extremal…
Consider a deterministic self-adjoint matrix X_n with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by…
In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…
We introduce and study several affine (=annular in this paper) versions of the classical diagram algebras such as Temperley-Lieb, partition, Brauer, Motzkin, rook Brauer, rook, planar partition, and planar rook algebras. We give generators…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we…
We characterize the atomic probability measure on $\mathbb{R}^d$ which having a finite number of atoms. We further prove that the Jacobi sequences associated to the multiple Hermite (resp. Laguerre, resp. Jacobi) orthogonal polynomials are…