For the real spherical ensemble, asymptotic formulas are derived for the probability of M real eigenvalues when M ~ N, M ~ sqrt(N), and M near the mean, with cross-regime matching and the leading p_{N,0} ~ e^{-sqrt(pi N/8) zeta(3/2)}.
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Asymptotics of the real eigenvalue distribution for the real spherical ensemble
For the real spherical ensemble, asymptotic formulas are derived for the probability of M real eigenvalues when M ~ N, M ~ sqrt(N), and M near the mean, with cross-regime matching and the leading p_{N,0} ~ e^{-sqrt(pi N/8) zeta(3/2)}.