Eur. Phys. J. B 4, 89-94 (1998)
https://doi.org/10.1007/s100510050354

Towards an universal classification of scale invariant processes

¹ CNRS (URA 2052) , CEA/DSM/DAPNIA/Service d'Astrophysique, CE Saclay, 91191 Gif-sur-Yvette, France
² CNRS (URA 285) , Observatoire Midi-Pyrénées, 14 avenue Belin, 31400 Toulouse, France
³ CEA/DSM/LMCE, CE Saclay, 91191 Gif-sur-Yvette, France
⁴ CNRS (UMR 5588) , Laboratoire de Spectrométrie Physique, Université Grenoble I, BP 87, 38402 Saint-Martin-d'Hères, France
⁵ IRPHE (UMR 6594 CNRS) , Universités Aix-Marseille I & II, Centre de Saint-Jérôme, S.252, 13397 Marseille, France

Corresponding author: ^a Graner@ujf-grenoble.fr

Received: 7 November 1997
Revised: 26 March 1998
Accepted: 30 March 1998
Published online: 15 July 1998

Abstract

We consider fields which take random values over several decades. Starting from physical examples, we postulate that scale is not an absolute quantity. We then establish the equivalence between two existing approaches based on scale symmetry arguments as general as possible. This yields a classification of log-infinitely divisible laws, possibly universal. The physical significance of the parameters entering in the classification is discussed.