Analysis of the large‐n limit of multiple orthogonal polynomials and non‐intersecting Brownian motions

Analysis of the large‐n limit of multiple orthogonal polynomials and non‐intersecting Brownian motions

In this work, we use the connection between families of multiple orthogonal polynomials with respect to a certain set of weights and random matrix models with external sources to determine the eigenvalue density and its support in the large‐n limit. These results are also applied to a model of non‐i...

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Veröffentlicht in:Mathematical methods in the applied sciences 2018-10, Vol.41 (15), p.5858-5868
Hauptverfasser: Alonso, L. Martínez, Medina, E.
Format: Artikel
Sprache:eng
Schlagworte:
Brownian motion
Brownian motions
Eigenvalues
Lax–Orlov operators
orthogonal polynomials
Polynomials
random matrix models
Riemann–Hilbert problems
string equation
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Zusammenfassung:In this work, we use the connection between families of multiple orthogonal polynomials with respect to a certain set of weights and random matrix models with external sources to determine the eigenvalue density and its support in the large‐n limit. These results are also applied to a model of non‐intersecting Brownian motions starting from a fix point. Copyright © 2010 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.1392