Multiple hermite polynomials and their applications in Random matrices with external source
| Item type | Current location | Call number | Copy number | Status | Date due | Barcode |
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Memoire
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Bibliothèque Centrale | 514.HAT.2020 (Browse shelf) | 1 | Not For Loan | 5010000364120 |
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Mémoire présenté et défendu publiquement en vue d'obtenir le diplôme de master en Mathématiques fondamentales et appliquées
Résumé,
Multiple orthogonal polynomials are polynomials of one variable which are defined by orthogonality relations with respect to different measure u1...u2...ur where r > 1 is a positive integer. Multiple hermite polyniomials play an important role in analysing random matrices with external source and also in the analysis of non intersecting Brownian motions leaving from one point and ariving at r distinct points. In this work, we focus on random matrices with external source and we show that multiple hermite polynomials belong to a problem of such a matrix ensemble and we give some applications of multiple Hermite polynomials. The main contributions of this work are contained in Theorem 3.0.3 of the Chapter 3 where we corrected the Theorem 2.4. of the paper of Lee, we also give two other proofs for the generating function and in Chapter 6 where we derived the asymptotic behaviors of multiple Hermite polynomials in region Il and III inside of the disk D (z1,r) of the complex plane.
Key words : multiple Hermite polynomials, generating function, random matrices with external source, Riemann-Hilbert problem, asymptotic behavior.
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