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- W2029209810 abstract "Nous considérons une marche aléatoire standard sur Z, partant de l'origine. Nous construisons une loi de probabilité sur Z en évaluant, pour chaque N⩾0 et k∈Z, le carré du nombre de trajectoires possibles se terminant au niveau k en N transitions ou moins. Nous normalisons ensuite ce nombre carré par sa somme, relativement à k, pour obtenir une loi de probabilité, dépendant de N. Notre résultat principal montre que cette loi de probabilité est asymptotiquement normale lorsque N→∞. Cette construction est inspirée par le modèle de base associé à l'interprétation de la mécanique quantique. Pour citer cet article : R. Charreton, C. R. Acad. Sci. Paris, Ser. I 345 (2007). 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)." @default.
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- W2029209810 date "2007-12-01" @default.
- W2029209810 modified "2023-09-25" @default.
- W2029209810 title "Une loi limite pour les marches aléatoires avec des applications physiques" @default.
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- W2029209810 doi "https://doi.org/10.1016/j.crma.2007.10.046" @default.
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