The limiting Kac random polynomial and truncated random orthogonal matrices

Details The limiting Kac random polynomial and truncated random orthogonal matrices The limiting Kac random polynomial and truncated random orthogonal matrices

2010-09-15

arxiv.org/abs/1009.3066v1

Physics

Mathematical Physics

12 pages, no figures

Scientific paper

An exact calculation of the eigenvalue statistics of truncated random Haar distributed real orthogonal matrices has recently been carried out by Khoruzhenko, Sommers and Zyczkowski. We further develop this calculation, and use it to deduce a Pfaffian form of the correlations for the zeros of the limiting Kac random polynomial. This contrasts with the forms known from previous studies of the real zeros (a multidimensional Gaussian integral with the integrand multiplied by the absolute values of the variables) and the complex zeros (a Hafnian).

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