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Asymptotics of Selberg-like integrals: the unitary case and Newton’s interpolation formula. (English) Zbl 1314.81177
Summary: We investigate the asymptotic behavior of the Selberg-like integral \(\frac{1}{N!}\int_{[0,1]^N}x_1^p\prod_{i<j}(x_i-x_j)^2\prod_ix_i^{a-1}(1-x_i)^{b-1}dx_i,\), as \(N \to \infty\) for different scalings of the parameters \(a\) and \(b\) with \(N\). Integrals of this type arise in the random matrix theory of electronic scattering in chaotic cavities supporting \(N\) channels in the two attached leads. Making use of Newton’s interpolation formula, we show that an asymptotic limit exists and we compute it explicitly.
©2010 American Institute of Physics

MSC:
81V70 Many-body theory; quantum Hall effect
60B20 Random matrices (probabilistic aspects)
81Q50 Quantum chaos
81V80 Quantum optics
65D05 Numerical interpolation
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