Weighted p-radial distributions on Euclidean and matrix p-balls with applications to large deviations

A probabilistic representation for a class of weighted p-radial distributions, based on mixtures cone probability measure and uniform distribution the Euclidean ℓpn-ball, is derived. Large deviation principles empirical coordinates random vectors ℓpn-ball with from this are discussed. The distributions extended to p-balls in classical matrix spaces, both self-adjoint non-self-adjoint matrices. eigenvalue matrix, chosen p-ball according such distribution, determined. Similarly, singular value identified case. Again, large spectral measures eigenvalues values presented as an application.