Zobrazeno 1 - 10
of 155
pro vyhledávání: '"Arnò, B."'
We consider orthogonal polynomials with respect to the weight $|z^2+a^2|^{cN}e^{-N|z|^2}$ in the whole complex plane. We obtain strong asymptotics and the limiting normalized zero counting measure (mother body) of the orthogonal polynomials of degree
Externí odkaz:
http://arxiv.org/abs/2408.12952
We compare two methods for analysing periodic dimer models. These are the matrix-valued orthogonal polynomials approach due to Duits and one of the authors, and the Wiener-Hopf approach due to Berggren and Duits. We establish their equivalence in the
Externí odkaz:
http://arxiv.org/abs/2402.07706
Autor:
Kuijlaars, Arno B. J.
Publikováno v:
Journal of Approximation Theory 288 (2023), 105875
The $n$-grid $E_n$ consists of $n$ equally spaced points in $[-1,1]$ including the endpoints $\pm 1$. The extremal polynomial $p_n^*$ is the polynomial that maximizes the uniform norm $\| p \|_{[-1,1]}$ among polynomials $p$ of degree $\leq \alpha n$
Externí odkaz:
http://arxiv.org/abs/2301.01591
Publikováno v:
SIGMA 19 (2023), 020, 18 pages
A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same poly
Externí odkaz:
http://arxiv.org/abs/2212.06526
We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann-Hilbert formulation for MVOPs and the Deift-Zhou method of ste
Externí odkaz:
http://arxiv.org/abs/2210.00797
Critical measures in the complex plane are saddle points for the logarithmic energy with external field. Their local and global structure was described by Martinez-Finkelshtein and Rakhmanov. In this paper we start the development of a theory of crit
Externí odkaz:
http://arxiv.org/abs/2207.02068
Autor:
Groot, Alan, Kuijlaars, Arno B. J.
Publikováno v:
Constructive Approximation 55 (2022), 775--827
In this paper, we study a class of matrix-valued orthogonal polynomials (MVOPs) that are related to 2-periodic lozenge tilings of a hexagon. The general model depends on many parameters. In the cases of constant and $2$-periodic parameter values we s
Externí odkaz:
http://arxiv.org/abs/2104.14822
We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by r+1 equal point charges that are symmetrically located around the north pole. The support of the equilibrium measure is known as the drop
Externí odkaz:
http://arxiv.org/abs/2008.01017
We study the equilibrium measure on the two dimensional sphere in the presence of an external field generated by two equal point charges. The support of the equilibrium measure is known as the droplet. Brauchart et al. showed that the complement of t
Externí odkaz:
http://arxiv.org/abs/1907.04801
Publikováno v:
Communications in Mathematical Physics 378 (2020), 401--466
We study a one-parameter family of probability measures on lozenge tilings of large regular hexagons that interpolates between the uniform measure on all possible tilings and a particular fully frozen tiling. The description of the asymptotic behavio
Externí odkaz:
http://arxiv.org/abs/1907.02460