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A vector equilibrium problem for the two-matrix model in the quartic/quadratic case
CALTECH, Pasadena.ORCID iD: 0000-0002-7598-4521
2011 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 24, no 3, 951-993 p.Article in journal (Refereed) Published
Abstract [en]

We consider the two sequences of biorthogonal polynomials (p(k,n))(k=0)(infinity) and (q(k,n))(k=0)(infinity) related to the Hermitian two-matrix model with potentials V (x) = x(2)/2 and W(y) = y(4)/4 + ty(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.

Place, publisher, year, edition, pages
2011. Vol. 24, no 3, 951-993 p.
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URN: urn:nbn:se:kth:diva-93352DOI: 10.1088/0951-7715/24/3/012ISI: 000287230100013OAI: diva2:515713
QC 20120627Available from: 2012-04-14 Created: 2012-04-14 Last updated: 2012-06-27Bibliographically approved

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Duits, Maurice
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