Multivariate and matrix-variate analogues of Maxwell-Boltzmann and Raleigh densities

The Maxwell-Boltzmann and Raleigh densities are basic densities in many problems in Physics. A multivariate analogue and a rectangular matrix-variate analogue of these densities are explored in this article. The results may become useful in extending the usual theories, where these densities for the real scalar variable case occur, to multivariate and matrix variable situations. Various properties are studied and connection to the volumes of parallelotopes determined by p linearly independent random points in Euclidean n-space, n≥p, is also established. Structural decompositions of these random determinants and pathway extensions of Maxwell-Boltzmann and Raleigh densities are also considered.