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Hankel determinant and orthogonal polynomials for the Gaussian weight with a jump
 in “Integrable Systems and Random Matrices
"... Abstract. We obtain asymptotics in n for the ndimensional Hankel determinant whose symbol is the Gaussian multiplied by a steplike function. We use RiemannHilbert analysis of the related system of orthogonal polynomials to obtain our results. ..."
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Cited by 16 (7 self)
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Abstract. We obtain asymptotics in n for the ndimensional Hankel determinant whose symbol is the Gaussian multiplied by a steplike function. We use RiemannHilbert analysis of the related system of orthogonal polynomials to obtain our results.
Asymptotics of Laurent Polynomials of Even Degree Orthogonal with Respect to Varying Exponential Weights
, 2006
"... LetΛR denote the linear space overRspanned by zk, k∈Z. Define the real inner product (with varying exponential weights)〈·,·〉L:ΛR×Λ R→R, ( f, g)↦ → ∫ f (s)g(s) exp(−N V(s)) ds, N∈N, where R the external field V satisfies: (i) V is real analytic onR\{0}; (ii) limx→∞(V(x) / ln(x2 +1))=+∞; and (iii) ..."
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Cited by 3 (2 self)
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LetΛR denote the linear space overRspanned by zk, k∈Z. Define the real inner product (with varying exponential weights)〈·,·〉L:ΛR×Λ R→R, ( f, g)↦ → ∫ f (s)g(s) exp(−N V(s)) ds, N∈N, where R the external field V satisfies: (i) V is real analytic onR\{0}; (ii) limx→∞(V(x) / ln(x2 +1))=+∞; and (iii) limx→0(V(x) / ln(x−2 +1))=+∞. Orthogonalisation of the (ordered) base{1, z−1, z, z−2, z2,...,z −k, zk,...} with respect to〈·,·〉L yields the even degree and odd degree orthonormal Laurent polynomials {φm(z)} ∞ (2n):φ2n(z)=ξ m=0 −n z−n +···+ξ (2n) n zn,ξ (2n) n>0, andφ2n+1(z)=ξ (2n+1) −n−1 z−n−1 +···+ξ (2n+1) n zn,ξ (2n+1)>0. Define
A universality theorem for ratios of random characteristic polynomials
 J. Approx. Theory
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ASYMPTOTICS OF CHARACTERISTIC POLYNOMIALS OF WIGNER MATRICES AT THE EDGE OF THE SPECTRUM
, 2008
"... We investigate the asymptotic behaviour of the secondorder correlation function of the characteristic polynomial of a Hermitian Wigner matrix at the edge of the spectrum. We show that the suitably rescaled secondorder correlation function is asymptotically given by the Airy kernel, thereby genera ..."
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Cited by 2 (1 self)
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We investigate the asymptotic behaviour of the secondorder correlation function of the characteristic polynomial of a Hermitian Wigner matrix at the edge of the spectrum. We show that the suitably rescaled secondorder correlation function is asymptotically given by the Airy kernel, thereby generalizing the wellknown result for the Gaussian Unitary Ensemble (GUE). Moreover, we obtain similar results for realsymmetric Wigner matrices.
CHARACTERISTIC POLYNOMIALS OF SAMPLE COVARIANCE MATRICES
, 2009
"... We investigate the secondorder correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for a generating function, we reobtain several wellknown kernels from random matrix theory. ..."
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Cited by 2 (0 self)
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We investigate the secondorder correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for a generating function, we reobtain several wellknown kernels from random matrix theory.
Gaussian Unitary Ensemble or a singular Hankel
, 2007
"... Correlations of the characteristic polynomials in the ..."
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