Geodesic
Lattice motions of the Euclidean plane
Sbornik. Mathematics, Tome 37 (1980) no. 2, pp. 245-259 
V. M. Maksimov. Lattice motions of the Euclidean plane. Sbornik. Mathematics, Tome 37 (1980) no. 2, pp. 245-259. http://geodesic.mathdoc.fr/item/SM_1980_37_2_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The idea of lattice motions of the plane is introduced; these motions arise quite naturally from the point of view of probability. A complete description of such motions is given, from which follows their close connection with quadratic extensions of the field of rational numbers. Bibliography: 7 titles.

[1] B. V. Gnedenko, A. N. Kolmogorov, Predelnye raspredeleniya dlya summ nezavisimykh sluchainykh velichin, Gostekhizdat, Moskva–Leningrad, 1949

[2] Ch. Stone, “A local limit theorem for nonlattice multi-dimensional distribution functions”, Amer. Math. Stat., 36:2 (1965), 546–551 | DOI | MR | Zbl

[3] P. Baldi, Ph. Bougerol, P. Creppel, “Theorem central limit local sur les deplacements de $\mathbf R^d$”, C. r. Acad. scient. Paris, serie A, 283 (1976), 53–55 | MR | Zbl

[4] V. M. Maksimov, “Lokalnaya teorema dlya reshetchatykh dvizhenii evklidovoi ploskosti”, DAN SSSR, 237:6 (1977), 1277–1280 | MR | Zbl

[5] N. Ya. Vilenkin, “Besselevy funktsii i predstavleniya gruppy evklidovykh dvizhenii”, Uspekhi matem. nauk., XI:3(69) (1956), 69–112 | MR

[6] V. M. Maksimov, “Ravnomernoe raspredelenie tochek i lokalnaya teorema dlya sluchainykh dvizhenii”, DAN SSSR, 232:2 (1977), 284–287 | MR | Zbl

[7] D. A. Kazhdan, “Ravnomernoe raspredelenie na ploskosti”, Trudy Mosk. matem. ob-va, 14 (1965), 299–305 | Zbl