THE POISSON-DISTRIBUTION ON A FRACTAL

Although the galaxy distribution is observed to be scale invariant at some scales, it cannot be identified to a perfect fractal which is a m athematical idealization. In this letter we illustrate, by a simple ex ample, the fact that discretisation and finite sampling effects modify the expected properties of a fractal-like distribution : sampling an ideal fractal by a finite sequence of independent observations, we obt ain a Poisson distribution on a fractal. Analyzing its main properties , with emphasis on number counts probabilities and mean N-points corre lation functions, we illustrate these effects. Alhough this is not int ended to modelize the galaxy distribution, we point out some similarit ies which justify the interest of this distribution for tests on stati stical methods.