Eur. Phys. J. B 32, 513-525 (2003)
https://doi.org/10.1140/epjb/e2003-00131-6

Broad distribution effects in sums of lognormal random variables

Institut de Physique et Chimie des Matériaux de Strasbourg (CNRS (UMR 7504)) , and Université Louis Pasteur, 23 rue du Loess, BP 43, 67034 Strasbourg Cedex 2, France

Corresponding author: ^a romeo@ipcms.u-strasbg.fr

Received: 8 November 2002
Revised: 17 March 2003
Published online: 7 May 2003

Abstract

The lognormal distribution describing, e.g. e.g., exponentials of Gaussian random variables is one of the most common statistical distributions in physics. It can exhibit features of broad distributions that imply qualitative departure from the usual statistical scaling associated to narrow distributions. Approximate formulae are derived for the typical sums of lognormal random variables. The validity of these formulae is numerically checked and the physical consequences, e.g. e.g., for the current flowing through small tunnel junctions, are pointed out.