Information theoretic approach to statistical properties of multivariate Cauchy-Lorentz distributions

The Cauchy-Lorentz (CL) distribution has divergent lowest moments. This nec essarily leads to the fact that the information theoretic approach is essen tial for the study of its statistical properties. Here, correlation measure d by the mutual entropy, is discussed for the multivariate CL distribution. It is found that correlation obeys a simple scaling law with respect to th e dimensionality of the distribution. Then, regarding the CL distribution a s a power-law quantum wavepacket, the information entropic uncertainty rela tion is also discussed both analytically and numerically. It is found that the sum of the position and momentum information entropies tends to the val ue of the lower bound for large dimensions.