Geodesic
The central limit theorem for random motions of Euclidean space
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1967), pp. 100-108 
V. N. Tutubalin. The central limit theorem for random motions of Euclidean space. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1967), pp. 100-108. http://geodesic.mathdoc.fr/item/VMUMM_1967_6_a10/
@article{VMUMM_1967_6_a10,
     author = {V. N. Tutubalin},
     title = {The central limit theorem for random motions of {Euclidean} space},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {100--108},
     year = {1967},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1967_6_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Each element $g$ of the group $G$ of all Euclidean motions in $R^3$ can be represented as $g=au$, where $a$ is translation and $u$ is rotation. Consider a sequence $g_1,g_2,\dots, g_n,\dots$ of random independent identically distributed elements of $G$ and their product $$ g(n)=g_1g_2\dots g_n=a(n)u(n). $$ With natural restrictions the distribution of $\frac1{\sqrt n}a(n)$ tends to a normal distribution as $n\to\infty$, while the distribution of $u(n)$ tends to the normed Haar measure on the group of rotations.