A. L'opez-Garc'ia

activity

20142026

most citedThe normal matrix model with a monomial potential, a vector equilibrium problem, and multiple orthogonal polynomials on a star

15 citations · 32 across the 14 of their papers we have counts for

collaborators

15 papers

math.CA2026

Higher-order asymptotics for the energy of greedy sequences on the unit circle

Abey López-García, Erwin Miña-Díaz

For the Riesz and logarithmic energies, we consider a greedy sequence $(a_{n})_{n = 0}^{\infty}$ of points on the unit circle $S^{1}$ constructed in such a way that for every integer $N\ge…

math.CA2024

Relative asymptotics of multiple orthogonal polynomials for Nikishin systems of two measures

Abey López-García, Guillermo López Lagomasino

We study the relative asymptotics of two sequences of multiple orthogonal polynomials corresponding to two Nikishin systems of measures on the real line, the second one of which is…

math.CA2023

Asymptotics of the optimal values of potentials generated by greedy energy sequences on the unit circle

Abey López-García, Erwin Miña-Díaz

For the Riesz and logarithmic potentials, we consider greedy energy sequences $(a_{n})_{n = 0}^{\infty}$ on the unit circle $S^{1}$ , constructed in such a way that for every $n \geq 1$ , the…

math.CO2023

Matrix continued fractions associated with lattice paths, resolvents of difference operators, and random polynomials

J. Kim, A. López-García, V. A. Prokhorov

We begin our analysis with the study of two collections of lattice paths in the plane, denoted $D_{[n, i, j]}$ and $P_{[n, i, j]}$ . These paths consist of sequences…

math.CA2022

Non-standard Green energy problems in the complex plane

Abey López-García, Alexander Tovbis

We consider several non-standard discrete and continuous Green energy problems in the complex plane and study the asymptotic relations between their solutions. In the discrete sett…

math.CO2022

Lattice paths, vector continued fractions, and resolvents of banded Hessenberg operators

Abey López-García, Vasiliy A. Prokhorov

We give a combinatorial interpretation of vector continued fractions obtained by applying the Jacobi-Perron algorithm to a vector of $p \geq 1$ resolvent functions of a banded Hesse…

math.CA2021

Asymptotics of the minimum values of Riesz and logarithmic potentials generated by greedy energy sequences on the unit circle

Abey López-García, Ryan E. McCleary

In this work we investigate greedy energy sequences on the unit circle for the logarithmic and Riesz potentials. By definition, if $(a_{n})_{n = 0}^{\infty}$ is a greedy $s$ -energy seq…

math.PR2021

Characteristic polynomials of random banded Hessenberg matrices and Hermite-Padé approximation

Abey López-García, Vasiliy A. Prokhorov

We consider a class of random banded Hessenberg matrices with independent entries having identical distributions along diagonals. The distributions may be different for entries bel…

math.CA2020★ 6 cited

Asymptotics of greedy energy sequences on the unit circle and the sphere

Abey López-García, Ryan E. McCleary

For a parameter $λ > 0$ , we investigate greedy $λ$ -energy sequences $(a_{n})_{n = 0}^{\infty}$ on the unit sphere $S^{d} \subset R^{d + 1}$ , $d \geq 1$ , satisfying the defining pro…

math.CA2019

Nikishin systems on star-like sets: Ratio asymptotics of the associated multiple orthogonal polynomials, II

Abey López-García, Guillermo López Lagomasino

In this paper we continue the investigations initiated in \cite{LopLopstar} on ratio asymptotics of multiple orthogonal polynomials and functions of the second kind associated with…

math.PR2018

On random polynomials generated by a symmetric three-term recurrence relation

Abey López García, Vasiliy A. Prokhorov

We investigate the sequence $(P_{n} (z))_{n = 0}^{\infty}$ of random polynomials generated by the three-term recurrence relation $P_{n + 1} (z) = z P_{n} (z) - a_{n} P_{n - 1} (z)$ , $n \geq 1$ , w…

math.CA2016

Nikishin systems on star-like sets: Ratio asymptotics of the associated multiple orthogonal polynomials

Abey López-García, Guillermo López Lagomasino

We investigate the ratio asymptotic behavior of the sequence $(Q_{n})_{n = 0}^{\infty}$ of multiple orthogonal polynomials associated with a Nikishin system of $p \geq 1$ measures tha…

math.CA2016★ 11 cited

Nikishin systems on star-like sets: algebraic properties and weak asymptotics of the associated multiple orthogonal polynomials

Abey López-García, Erwin Miña-Díaz

Polynomials $Q_{n} (z)$ , $n = 0, 1, \dots,$ that are multi-orthogonal with respect to a Nikishin system of $p \geq 1$ compactly supported measures over the star-like set of $p + 1$ rays $S_…

math.CA2015

Asymptotics of the energy of sections of greedy energy sequences on the unit circle, and some conjectures for general sequences

Abey López-García, Douglas A. Wagner

In this paper we investigate the asymptotic behavior of the Riesz $s$ -energy of the first $N$ points of a greedy $s$ -energy sequence on the unit circle, for all values of $s$ in th…

math.CA2014★ 15 cited

The normal matrix model with a monomial potential, a vector equilibrium problem, and multiple orthogonal polynomials on a star

Arno B. J. Kuijlaars, Abey López-García

We investigate the asymptotic behavior of a family of multiple orthogonal polynomials that is naturally linked with the normal matrix model with a monomial potential of arbitrary d…