Asymptotics for Hankel Determinants Associated to a Hermite Weight with a Varying Discontinuity
| Autor: | Christophe Charlier, Alfredo Deaño |
|---|---|
| Přispěvatelé: | Ministerio de Economía y Competitividad (España), European Commission |
| Rok vydání: | 2018 |
| Předmět: |
Asymptotic analysis
Matemáticas Gaussian Mathematics::Classical Analysis and ODEs Riemann-Hilbert problems FOS: Physical sciences Painlevé equations 010103 numerical & computational mathematics 01 natural sciences Random matrix theory symbols.namesake Singularity Classical Analysis and ODEs (math.CA) FOS: Mathematics Complex Variables (math.CV) 0101 mathematics Real line Mathematical Physics Mathematics Hermite polynomials Mathematics - Complex Variables Probability (math.PR) 010102 general mathematics Mathematical analysis Mathematical Physics (math-ph) Function (mathematics) Discontinuity (linguistics) Mathematics - Classical Analysis and ODEs symbols Geometry and Topology Random matrix Analysis Mathematics - Probability Hankel determinants |
| Zdroj: | e-Archivo: Repositorio Institucional de la Universidad Carlos III de Madrid Universidad Carlos III de Madrid (UC3M) e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid instname |
| ISSN: | 1815-0659 |
| Popis: | This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14). The full collection is available at https://www.emis.de/journals/SIGMA/OPSFA2017.html We study nxn Hankel determinants constructed with moments of a Hermite weight with a Fisher-Hartwig singularity on the real line. We consider the case when the singularity is in the bulk and is both of root-type and jump-type. We obtain large n asymptotics for these Hankel determinants, and we observe a critical transition when the size of the jumps varies with n. These determinants arise in the thinning of the generalised Gaussian unitary ensembles and in the construction of special function solutions of the Painlevé IV equation. C. Charlier was supported by the European Research Council under the European Union's Seventh Framework Programme (FP/2007/2013)/ ERC Grant Agreement n. 307074. A. Deaño acknowledges financial support from projects MTM2012-36732-C03-01 and MTM2015-65888-C4-2-P from the Spanish Ministry of Economy and Competitivity. The authors are grateful to A.B.J. Kuijlaars for sharing a simplified proof for the first part of [11, Proposition A.1]. This inspired us to simplify the proof of Lemma 7.4. We also thank T. Claeys for a careful reading of the introduction and for useful remarks. The authors acknowledge the referees for their careful reading and useful remarks. Publicado |
| Databáze: | OpenAIRE |
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