A vector equilibrium problem for the two-matrix model in the quartic/quadratic case
2011 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 24, no 3, 951-993 p.Article in journal (Refereed) Published
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.
IdentifiersURN: urn:nbn:se:kth:diva-93352DOI: 10.1088/0951-7715/24/3/012ISI: 000287230100013OAI: oai:DiVA.org:kth-93352DiVA: diva2:515713
QC 201206272012-04-142012-04-142012-06-27Bibliographically approved