Title: Critical behavior in Angelesco ensembles
Authors: Deschout, Klaas ×
Kuijlaars, Arno #
Issue Date: Dec-2012
Publisher: American Institute of Physics
Series Title: Journal of Mathematical Physics vol:53 issue:12
Article number: 123523
Abstract: We consider Angelesco ensembles with respect to two modified Jacobi weights on touching intervals [a, 0] and [0, 1], for a < 0. As a → −1 the particles around 0 experience a phase transition. This transition is studied in a double scaling limit, where we let the number of particles of the ensemble tend to infinity while the parameter a tends to −1 at a rate of O(n^(−1/2)). The correlation kernel converges, in this regime, to a new kind of universal kernel, the Angelesco kernel. The result follows from the Deift/Zhou steepest descent analysis, applied to the Riemann-Hilbert problem for multiple orthogonal polynomials.
ISSN: 0022-2488
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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