ON THE LOCALITY OF LEVEL SPACING DISTRIBUTIONS

We use a generalisation of a formula introduced by Mehta to analyse th e dependence of the spacing distribution on the region of the spectrum . Such a dependence, which usually receives little attention, is howev er an important feature of the statistics of spacings. Our examples ar e physical systems constituted of the sum of non-interacting subsystem s whose spacing distributions obey the Poisson law; we have found that the spacing distributions of the total systems are quite complicated, even if their histograms may look approximately like exponentials. Th e formulae we have obtained for the local spacing distributions and fo r the means of such distributions have been tested by means of numeric al simulations obtaining a satisfactory consistence.