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138
The Cauchy twomatrix model
, 2002
"... We introduce a new class of two(multi)matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The correlation functions are expressed entirely in terms of certain bi ..."
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Cited by 17 (8 self)
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We introduce a new class of two(multi)matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The correlation functions are expressed entirely in terms of certain
Integrals of Rational Symmetric Functions, Two–Matrix Models and Biorthogonal Polynomials
, 2006
"... We give a new method for the evaluation of a class of integrals of rational symmetric functions in N pairs of variables {(xa,ya)}a=1,...N arising in coupled matrix models, valid for a broad class of twovariable measures. The result is expressed as the determinant of a matrix whose entries consist o ..."
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Cited by 1 (0 self)
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We give a new method for the evaluation of a class of integrals of rational symmetric functions in N pairs of variables {(xa,ya)}a=1,...N arising in coupled matrix models, valid for a broad class of twovariable measures. The result is expressed as the determinant of a matrix whose entries consist
The PDEs of biorthogonal polynomials . . .
, 2004
"... The twomatrix model can be solved by introducing biorthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of biorthogonal polynomials (called windows) satisfy polynomial ODEs as well as deformation equations (PDEs) and finite difference equations (∆E) ..."
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Cited by 1 (0 self)
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The twomatrix model can be solved by introducing biorthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of biorthogonal polynomials (called windows) satisfy polynomial ODEs as well as deformation equations (PDEs) and finite difference equations (∆E
The PDEs of biorthogonal polynomials arising in . . .
, 2003
"... The twomatrix model can be solved by introducing biorthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of biorthogonal polynomials (called windows) satisfy polynomial ODEs as well as deformation equations (PDEs) and finite difference equations (∆E) ..."
Abstract

Cited by 1 (0 self)
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The twomatrix model can be solved by introducing biorthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of biorthogonal polynomials (called windows) satisfy polynomial ODEs as well as deformation equations (PDEs) and finite difference equations (∆E
Biorthogonal polynomials for 2matrix . . .
, 2006
"... We consider the biorthogonal polynomials associated to the two–matrix model where the eigenvalue distribution has potentials V1, V2 with arbitrary rational derivative and whose supports are constrained on an arbitrary union of intervals (hardedges). We show that these polynomials satisfy certain re ..."
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We consider the biorthogonal polynomials associated to the two–matrix model where the eigenvalue distribution has potentials V1, V2 with arbitrary rational derivative and whose supports are constrained on an arbitrary union of intervals (hardedges). We show that these polynomials satisfy certain
Mixed Correlation Functions of the TwoMatrix Model
, 2003
"... We compute the correlation functions mixing the powers of two noncommuting random matrices within the same trace. The angular part of the integration was partially known in the literature [16, 17]: we pursue the calculation and carry out the eigenvalue integration reducing the problem to the constr ..."
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to the construction of the associated biorthogonal polynomials. The generating function of these correlations becomes then a determinant involving the recursion coefficients of the biorthogonal polynomials.
Semiclassical asymptotics of orthogonal polynomials, RiemannHilbert problem, and universality in the matrix model
, 1999
"... We derive semiclassical asymptotics for the orthogonal polynomials Pn(z) on the line with respect to the exponential weight exp(−NV (z)), where V (z) is a doublewell quartic polynomial, in the limit when n,N → ∞. We assume that ε ≤ (n/N) ≤ λcr − ε for some ε> 0, where λcr is the critical value ..."
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Cited by 166 (11 self)
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which separates orthogonal polynomials with two cuts from the ones with one cut. Simultaneously we derive semiclassical asymptotics for the recursive coefficients of the orthogonal polynomials, and we show that these coefficients form a cycle of period two which drifts slowly with the change
Cauchy biorthogonal polynomials
 J. Approx. Theory
"... Peakons are nonsmooth soliton solutions appearing in certain nonlinear partial differential equations, most notably the CamassaHolm equation and the DegasperisProcesi equation. In the latter case the construction of peakons leads to a new class of biorthogonal polynomials. The present paper is t ..."
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Cited by 11 (4 self)
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of these polynomials to a third order boundary value problem (the cubic string) is explained. Moreover a connection to certain twomatrix random matrix models, elaborated on in subsequent papers, is pointed out.
Chiral Random TwoMatrix Theory and QCD with imaginary chemical potential ∗
, 710
"... We summarise recent results for the chiral Random TwoMatrix Theory constructed to describe QCD in the epsilonregime with imaginary chemical potential. The virtue of this theory is that unquenched Lattice simulations can be used to determine both low energy constants Σ and F in the leading order ch ..."
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We summarise recent results for the chiral Random TwoMatrix Theory constructed to describe QCD in the epsilonregime with imaginary chemical potential. The virtue of this theory is that unquenched Lattice simulations can be used to determine both low energy constants Σ and F in the leading order
Results 1  10
of
138