Une loi limite pour les marches aléatoires avec des applications physiques

Abstract

We consider a standard random walk on Z , starting from the origin. We build a law of probability on Z , based upon the evaluation, for each N ⩾ 0 and k ∈ Z , of the squared number of possible trajectories, reaching level k after N or less transitions. We normalize this squared number by its sum, with respect to k, to obtain a probability law, depending upon N. Our main result establishes that this probability law converges to a normal distribution as N → ∞ . Our construction is inspired and motivated by the basic model used for the interpretation of quantum mechanics. To cite this article: R. Charreton, C. R. Acad. Sci. Paris, Ser. I 345 (2007).