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Solution of a Riemann–Hilbert problem for a new expression of

✍ Scribed by Rabindra Nath Das


Publisher
Springer Netherlands
Year
2008
Tongue
English
Weight
266 KB
Volume
317
Category
Article
ISSN
0004-640X

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We find a local (d + 1) × (d + 1) Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of orthogonal ensembles of random matrices with a potential function of degree d. Our Riemann-Hilbert problem is similar to a local d × d Riemann-Hilbert prob

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where ~( 5 ) is a rational function. ## Bibliography [I] Pogorzelski, W., Integral Equations and their Applications, Pergamon Press, 1966, (see the references [2] Peters, A. S., Pairs o f Cauchy singular integral equations and the kernel [ b ( z ) f a ( { ) ] / ( z -{), at the end of this book).