Asymptotics of special functions and the central limit theorem on the space [Weierstrass p]n of positive n - n matrices

When n = 3 using methods similar to the author's (1984, J. Multivariate Anal.15, 261-276), an analog of the central limit theorem is obtained for rotation-invariant random variables on the space[Weierstrass p]n of positive n - n real matrices (the symmetric space of the general linear group GL(n,[real]) of n - n nonsingular real matrices). The necessary results from harmonic analysis onPn are sketched.