{"id":8,"date":"2018-01-03T16:49:51","date_gmt":"2018-01-03T21:49:51","guid":{"rendered":"https:\/\/sciencescosmaincms.cm.ucf.edu\/math\/lopez-garcia\/?page_id=8"},"modified":"2026-04-14T21:49:47","modified_gmt":"2026-04-15T01:49:47","slug":"research","status":"publish","type":"page","link":"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/research\/","title":{"rendered":"Research"},"content":{"rendered":"<p>I do research in Analysis. My current research interests are concentrated in the following areas:<\/p>\n<ul>\n<li>Multiorthogonal polynomials<\/li>\n<li>Minimal energy problems and Potential Theory<\/li>\n<li>Random matrices and random polynomials<\/li>\n<\/ul>\n<p>A list of my publications and preprints is given here:<\/p>\n<ol>\n<li>A. L\u00f3pez-Garc\u00eda and E. Mi\u00f1a-D\u00edaz, <span style=\"color: #3439c7\"><i>Higher-order asymptotics for the energy of greedy sequences on the unit circle<\/i><span style=\"color: #000000\">, arXiv:<span data-olk-copy-source=\"MessageBody\">2604.12226,<\/span><span style=\"color: #333333\"> 44 pp. [<a href=\"https:\/\/arxiv.org\/abs\/2604.12226\">arXiv<\/a>]<\/span><\/span><\/span><\/li>\n<li>A. L\u00f3pez Garc\u00eda and G. L\u00f3pez Lagomasino, <i style=\"color: #3439c7\">Relative\u00a0<\/i><span style=\"color: #3439c7\"><i>asymptotics of multiple orthogonal polynomials for Nikishin systems of two measures<\/i><span style=\"color: #000000\"><span style=\"color: #333333\">, J. Approx. Theory 309 (2025) 106158, 19 pp<\/span><\/span><span style=\"color: #000000\"><span style=\"color: #333333\">.<\/span> [<a href=\"https:\/\/arxiv.org\/abs\/2407.16738\">arXiv<\/a>]<\/span><\/span><\/li>\n<li>A. L\u00f3pez-Garc\u00eda and E. Mi\u00f1a-D\u00edaz, <span style=\"color: #3439c7\"><i>Asymptotics of the optimal values of potentials generated by greedy energy sequences on the unit circle<\/i><span style=\"color: #000000\">, <span style=\"color: #333333\">J. Math. Anal. Appl. 538 (2024) 128401, 20 pp.\u00a0<\/span><\/span><\/span><span style=\"color: #3439c7\"><span style=\"color: #000000\">[<a href=\"https:\/\/arxiv.org\/abs\/2309.04387\">arXiv<\/a>]<\/span><\/span><\/li>\n<li>J. Kim, A. L\u00f3pez-Garc\u00eda, and V.A. Prokhorov, <span style=\"color: #3439c7\"><i>Matrix continued fractions associated with lattice paths, resolvents of difference operators, and random polynomials<\/i><span style=\"color: #000000\">, <span style=\"color: #333333\">Constr. Approx. 62 (2025), 185-242<\/span><\/span><span style=\"color: #000000\"><span style=\"color: #333333\">.<\/span> [<a href=\"https:\/\/arxiv.org\/abs\/2307.02619\">arXiv<\/a>]<\/span><\/span><\/li>\n<li>A. L\u00f3pez-Garc\u00eda and A. Tovbis, <span style=\"color: #3439c7\"><i>Non-standard Green energy problems in the complex<\/i> plane<span style=\"color: #333333\">, Anal. Math<\/span><span style=\"color: #000000\"><span style=\"color: #333333\">. Phys. 13, 77 (2023), 36 pp.<\/span>\u00a0[<a href=\"https:\/\/arxiv.org\/abs\/2211.07053\">arXiv<\/a>]<\/span><\/span><\/li>\n<li>A. L\u00f3pez-Garc\u00eda and V.A. Prokhorov, <span style=\"color: #3439c7\"><i>Lattice paths, vector continued fractions, and resolvents of banded Hessenberg operators<\/i><\/span><span style=\"color: #333333\"><em>, <\/em>Comput. Methods Funct. Theory 24 (2024), 769-809<\/span><span style=\"color: #000000\"><span style=\"color: #333333\">.<\/span> [<a href=\"https:\/\/arxiv.org\/abs\/2203.00243\">arXiv<\/a>]<\/span><\/li>\n<li>A. L\u00f3pez-Garc\u00eda and R.E. McCleary, <span style=\"color: #3439c7\"><i>Asymptotics of the minimum values of Riesz and logarithmic potentials generated by greedy energy sequences on the unit circle<span style=\"color: #333333\">,<\/span><\/i><span style=\"color: #333333\">\u00a0J. Math. Anal. Appl<\/span><span style=\"color: #000000\"><span style=\"color: #333333\">. 508 (2022) 125866, 36 pp.<\/span> [<a href=\"https:\/\/arxiv.org\/abs\/2105.10817\">arXiv<\/a>]<\/span><\/span><\/li>\n<li>A. L\u00f3pez-Garc\u00eda and V.A. Prokhorov, <span style=\"color: #3439c7\"><i>Characteristic polynomials of random banded Hessenberg matrices and Hermite-Pad\u00e9 approximation,<\/i>\u00a0<span style=\"color: #000000\">Complex Anal. Oper. Theory 15:113 (2021), 25 pp<\/span><span style=\"color: #000000\">. [<a href=\"https:\/\/arxiv.org\/abs\/2104.03456\">arXiv<\/a>]<\/span><\/span><\/li>\n<li>A. L\u00f3pez-Garc\u00eda and R.E. McCleary, <span style=\"color: #3439c7\"><i>Asymptotics of greedy energy sequences on the unit circle and the sphere<\/i><\/span>, J. Math. Anal. Appl. 504 (2021) 125269, 35 pp. [<a href=\"https:\/\/arxiv.org\/abs\/2007.06109\">arXiv<\/a>]<\/li>\n<li>A. L\u00f3pez-Garc\u00eda and G. L\u00f3pez Lagomasino, <i><span style=\"color: #3439c7\">Nikishin systems on star-like sets: Ratio asymptotics of the associated multiple orthogonal polynomials, II<\/span>, <\/i>J. Approx. Theory 250 (2020) 105320, 28 pp. [<a href=\"https:\/\/arxiv.org\/abs\/1907.03002\">arXiv<\/a>]<\/li>\n<li>A. L\u00f3pez-Garc\u00eda and V.A. Prokhorov, <i><span style=\"color: #3439c7\">On random polynomials generated by a symmetric three-term recurrence relation<\/span>, <\/i>J. Difference Equations Appl. 25 (2019), 1604-1643. [<a href=\"https:\/\/arxiv.org\/abs\/1804.03205\">arXiv<\/a>]<\/li>\n<li>A. L\u00f3pez-Garc\u00eda and G. L\u00f3pez Lagomasino,\u00a0<span style=\"color: #3439c7\"><em>Nikishin systems on star-like sets: Ratio asymptotics of the associated multiple orthogonal polynomials<\/em><\/span><i>,\u00a0<\/i>J. Approx. Theory 225 (2018), 1-40. [<a href=\"https:\/\/arxiv.org\/abs\/1612.01149\">arXiv<\/a>]<\/li>\n<li>A. L\u00f3pez-Garc\u00eda and E. Mi\u00f1a-D\u00edaz, <span style=\"color: #3439c7\"><em>Nikishin systems on star-like sets: algebraic properties and weak asymptotics of the associated multiple orthogonal polynomials<\/em><\/span><i>, <\/i>(Russian) Mat. Sb. 209 (2018), 139-177; English transl., Sb. Math. 209 (2018), 1051-1088. [<a href=\"https:\/\/arxiv.org\/abs\/1606.08047\">arXiv<\/a>]<\/li>\n<li>A. L\u00f3pez-Garc\u00eda and D.A. Wagner,\u00a0<i><span style=\"color: #3439c7\">Asymptotics of the energy of sections of greedy energy sequences on the unit circle, and some conjectures for general sequences<\/span>,\u00a0<\/i>Comput. Methods Funct. Theory 15 (2015), 721-750. [<a href=\"https:\/\/arxiv.org\/abs\/1502.00063\">arXiv<\/a>]<\/li>\n<li>A.B.J. Kuijlaars and A.\u00a0L\u00f3pez-Garc\u00eda,\u00a0<i><span style=\"color: #3439c7\">The normal matrix model with a monomial potential, a vector equilibrium problem, and multiple orthogonal polynomials on a star<\/span>,\u00a0<\/i>Nonlinearity 28 (2015), 347-406. [<a href=\"https:\/\/arxiv.org\/abs\/1401.2419v2\">arXiv<\/a>]<\/li>\n<li>S. Delvaux and A. L\u00f3pez,\u00a0 <i><span style=\"color: #3439c7\">High-order three-term recursions, Riemann-Hilbert minors and Nikishin systems on star-like sets<\/span>,\u00a0<\/i>Constr. Approx. 37 (2013), 383-453. [<a href=\"https:\/\/arxiv.org\/abs\/1202.4000\">arXiv<\/a>]<\/li>\n<li>S. Delvaux, A. L\u00f3pez and G. L\u00f3pez Lagomasino, \u00a0<i><span style=\"color: #3439c7\">A family of Nikishin systems with periodic recurrence coefficients<\/span>, <\/i>(Russian) Mat. Sb.\u00a0204 (2013), 47-78; English transl., Sb. Math. 204 (2013), 43-74. [<a href=\"https:\/\/arxiv.org\/abs\/1110.3032\">arXiv<\/a>]<\/li>\n<li>\u00a0A. L\u00f3pez Garc\u00eda, <span style=\"color: #3439c7\"><em>Asymptotics of multiple orthogonal polynomials for a system of two measures supported on a starlike set<\/em><\/span>, J. Approx. Theory 163 (2011), 1146-1184. [<a href=\"https:\/\/arxiv.org\/abs\/1009.0466\">arXiv<\/a>] [<a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2019\/09\/Lopstar.pdf\">article<\/a>]<\/li>\n<li>A. L\u00f3pez Garc\u00eda and E.B. Saff, <span style=\"color: #3439c7\"><em>Asymptotics of Greedy Energy Points<\/em><\/span>, Math. Comp. 79 (2010), 2287-2316. [<a href=\"https:\/\/arxiv.org\/abs\/0901.3840\">arXiv<\/a>] [<a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2019\/09\/Asymptotics-of-Greedy-Energy-Points.pdf\">article<\/a>]<\/li>\n<li>A. L\u00f3pez Garc\u00eda, <span style=\"color: #3439c7\"><em>Greedy energy points with external fields<\/em><\/span>, in &#8220;Recent Trends in Orthogonal Polynomials and Approximation Theory&#8221; (J. Arves\u00fa, F. Marcell\u00e1n, and A. Mart\u00ednez-Finkelshtein, eds.), Contemp. Math. 507, 2010, 189-207. [<a href=\"https:\/\/arxiv.org\/abs\/0901.4160\">arXiv<\/a>]<\/li>\n<li>U. Fidalgo Prieto, A. L\u00f3pez Garc\u00eda, G. L\u00f3pez Lagomasino, and V.N. Sorokin, <span style=\"color: #3439c7\"><em>Mixed type multiple orthogonal polynomials for two Nikishin systems<\/em><\/span>, Constr. Approx. 32 (2010), 255-306. [<a href=\"https:\/\/arxiv.org\/abs\/0812.1219\">arXiv<\/a>]<\/li>\n<li>A. L\u00f3pez Garc\u00eda and G. L\u00f3pez Lagomasino, <span style=\"color: #3439c7\"><em>Relative asymptotic of multiple orthogonal polynomials for Nikishin systems<\/em><\/span>, J. Approx. Theory 158 (2009), 214-241. [<a href=\"https:\/\/arxiv.org\/abs\/0802.0722\">arXiv<\/a>] [<a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2019\/09\/Relative-asymptotic-of-multiple-orthogonal-polynomials-for-Nikishin-systems.pdf\">article<\/a>]<\/li>\n<li>A. L\u00f3pez Garc\u00eda and G. L\u00f3pez Lagomasino, <span style=\"color: #3439c7\"><em>Ratio asymptotic of Hermite-Pad\u00e9 orthogonal polynomials for Nikishin systems. II<\/em><\/span>, Adv. Math. 218 (2008), 1081-1106. [<a href=\"https:\/\/arxiv.org\/abs\/0707.1996\">arXiv<\/a>] [<a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2019\/09\/LopLopRatioLine.pdf\">article<\/a>]<\/li>\n<li>M.A. Jim\u00e9nez Pozo and A. L\u00f3pez Garc\u00eda, <span style=\"color: #3439c7\"><em>Aplicaciones del \u00c1lgebra de Boole m\u00e9trica a la Teor\u00eda de la Medida<\/em><\/span>, La Gaceta de la RSME 9.1 (2006), 59-68.<\/li>\n<\/ol>\n<p>The following are some pdf files of conference and seminar presentations:<\/p>\n<ul>\n<li><a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2025\/08\/TalkGreedyALGNashville.pdf\">Asymptotics of the optimal values of potentials generated by greedy energy sequences on the unit circle<\/a>, Constructive Functions 2025, conference in honor of Ed Saff, Vanderbilt University, May 19-22, 2025.<\/li>\n<li><a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2025\/11\/TalkBaylorFestAbey.pdf\">Lattice paths, vector continued fractions, and resolvents of banded Hessenberg operators<\/a>, Baylor Analysis Fest, conference in honor of Lance L. Littlejohn, Baylor University, May 23-27, 2022.<\/li>\n<li><a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2022\/03\/CMStalk.pdf\">Spectral properties of random banded Hessenberg matrices<\/a>, 2021 Canadian Mathematical Society Winter Meeting, December 2-7, 2021.<\/li>\n<li><a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2020\/09\/CAOPAtalk.pdf\">Asymptotics of greedy energy sequences on the unit circle and the sphere<\/a>, in CAOPA Zoom seminar, Moscow, September 7, 2020.<\/li>\n<li><a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2025\/11\/TalkALGAustria.pdf\">Nikishin systems on star-like sets: limiting functions in ratio asymptotics<\/a>, in 15th International Symposium on Orthogonal Polynomials, Special Functions, and Applications, Hagenberg, Austria, July 22-26, 2019.<\/li>\n<li><a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-content\/uploads\/sites\/26\/2018\/09\/TalkJaenALG.pdf\">Random polynomials generated by a three-term recurrence relation<\/a>, in IX Ja\u00e9n Conference on Approximation Theory, \u00dabeda, Spain, July 8-13, 2018.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>I do research in Analysis. My current research interests are concentrated in the following areas: Multiorthogonal polynomials Minimal energy problems and Potential Theory Random matrices and random polynomials A list of my publications and preprints is given here: A. L\u00f3pez-Garc\u00eda and E. Mi\u00f1a-D\u00edaz, Higher-order asymptotics for the energy of greedy sequences on the unit circle, &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/research\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Research&#8221;<\/span><\/a><\/p>\n","protected":false},"author":34,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-8","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-json\/wp\/v2\/pages\/8","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-json\/wp\/v2\/users\/34"}],"replies":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-json\/wp\/v2\/comments?post=8"}],"version-history":[{"count":38,"href":"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-json\/wp\/v2\/pages\/8\/revisions"}],"predecessor-version":[{"id":220,"href":"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-json\/wp\/v2\/pages\/8\/revisions\/220"}],"wp:attachment":[{"href":"https:\/\/sciences.ucf.edu\/math\/lopez-garcia\/wp-json\/wp\/v2\/media?parent=8"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}