Geodesic
The group of diffeomorphisms of the half-line, and random Cantor sets
Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 857-868 
Yu. A. Neretin. The group of diffeomorphisms of the half-line, and random Cantor sets. Sbornik. Mathematics, Tome 187 (1996) no. 6, pp. 857-868. http://geodesic.mathdoc.fr/item/SM_1996_187_6_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A certain one-parameter family of measures is constructed on the space of closed totally disconnected subsets of the half-line without isolated points. It is shown that these measures are quasi-invariant with respect to the group of smooth diffeomorphisms of the half-line, and the Radon–Nikodym derivatives are explicitly computed.

[1] Vershik A. M., Gelfand I. M., Graev M. I., “Predstavleniya grupp diffeomorfizmov”, UMN, 30:6 (1975), 1–50 | MR | Zbl

[2] Dynkin E. B., “Nekotorye predelnye teoremy dlya summ nezavisimykh sluchainykh velichin s beskonechnymi matematicheskimi ozhidaniyami”, Izv. AN SSSR. Ser. matem., 19 (1955), 247–266 | MR | Zbl

[3] Zolotarev V. M., Odnomernye ustoichivye raspredeleniya, Nauka, M., 1983 | MR

[4] Ismagilov R. S., “Ob unitarnykh predstavleniyakh gruppy diffeomorfizmov okruzhnosti”, Funkts. analiz i prilozh., 5:3 (1971), 45–53 | MR | Zbl

[5] Ito K., Makkin G., Diffuzionnye protsessy i ikh traektorii, Mir, M., 1968 | Zbl

[6] Kerstan I., Mattes K., Mekke I., Bezgranichno delimye tochechnye protsessy, Nauka, M., 1982 | MR | Zbl

[7] Levi P., Stokhasticheskie protsessy i brounovskoe dvizhenie, Nauka, M., 1972 | MR

[8] Lukach E., Kharakteristicheskie funktsii, Nauka, M., 1979 | MR | Zbl

[9] Neretin Yu. A., “Kategorii bistokhasticheskikh mer i predstavleniya nekotorykh beskonechnomernykh grupp”, Matem. sb., 183:2 (1992), 52–76 | MR

[10] Skorokhod A. V., Sluchainye protsessy s nezavisimymi prirascheniyami, Nauka, M., 1986 | MR

[11] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, T. 2, Mir, M., 1967

[12] Shavgulidze E. T., “O mere, kvaziinvariantnoi po otnosheniyu k deistviyu gruppy diffeomorfizmov konechnomernogo mnogoobraziya”, DAN SSSR, 303:4 (1988), 811–814 | MR

[13] Geman D., Horowitz G., “Occupation densities”, Ann. Probab., 8:1 (1980), 1–67 | DOI | MR | Zbl

[14] Kahane J. P., Some random series of functions, Cambridge Univ. Press, Cambridge, 1985 | MR | Zbl

[15] Kerov S. V., Olshanskii G. I., Vershik A. M., “Harmonic analysis on the infinite symmetric group”, C. R. Acad. Sci. Paris. Sér. I Math., 316 (1993), 773–778 | MR | Zbl

[16] Neretin Yu. A., “Some remarks on quasi-invariant actions of loop groups and the group of diffeomorphisms of the circle”, Comm. Math. Phys., 164:2 (1994), 599–626 | DOI | MR | Zbl

[17] Neretin Yu. A., “Mantles, trains and representations of infinite dimensional groups”, First European Congress of Math., V. 2, Birkhauser, 1994, 293–310 | MR | Zbl

[18] Olshanskii G. I., “On semigroups related to infinite dimensional groups”, Topics in representation theory, Adv. Sov. Math., 2, ed. A. A. Kirillov, 1991, 67–101 | MR

[19] Orey S., “Gaussian sample functions and Hausdorff dimension of level sets”, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 15 (1970), 249–256 | DOI | MR | Zbl

[20] Pickrell D., “Measures on infinite dimensional grassmann manifold”, J. Funct. Anal., 70 (1987), 323–336 | DOI | MR

[21] Revuz D., Yor M., Continuous martingales and Brownian motion, Springer-Verlag, Berlin, 1991 | MR | Zbl

[22] Voiculescu D. V., Dikema K. J., Nica A., Free random variables, Amer. Math. Soc., Providence, 1993 | MR | Zbl