Title: A vector equilibrium problem for the two-matrix model in the quartic/quadratic case
Authors: Duits, Maurice
Geudens, Dries
Kuijlaars, Arno # ×
Issue Date: Mar-2011
Publisher: IOP Pub.
Series Title: Nonlinearity vol:24 issue:3 pages:951-993
Abstract: We consider the two sequences of biorthogonal polynomials (p_{k,n})_k and (q_{k,n})_k related to the Hermitian two-matrix model with potentials V(x) = x^2/2 and W(y) = y^4/4 + t y^2. From an asymptotic analysis of the coefficients in the recurrence relation satisfied by these polynomials, we obtain the limiting distribution of the zeros of the polynomials p_{n,n} as n -> infinity. The limiting zero distribution is characterized as the first measure of the minimizer in a vector equilibrium problem involving three measures which for the case t = 0 reduces
to the vector equilibrium problem that was given recently by two of us. A novel feature is that for t < 0 an external field is active on the third measure which introduces a new type of critical behaviour for a certain negative value of t.

We also prove a general result about the interlacing of zeros of biorthogonal polynomials.
ISSN: 0951-7715
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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