Keywords: probabilistic number theory, Bose–Einstein distribution, Zipf law, thermodynamics, negative dimension.
@article{TMF_2007_150_1_a6,
author = {V. P. Maslov},
title = {Zeroth-order phase transitions and {Zipf} law quantization},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {118--142},
year = {2007},
volume = {150},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2007_150_1_a6/}
}
V. P. Maslov. Zeroth-order phase transitions and Zipf law quantization. Teoretičeskaâ i matematičeskaâ fizika, Tome 150 (2007) no. 1, pp. 118-142. http://geodesic.mathdoc.fr/item/TMF_2007_150_1_a6/
[1] A. N. Kolmogorov, PPI, 5:3 (1969), 3–7 | MR | Zbl
[2] V. V. Vyugin, V. P. Maslov, PPI, 39:4 (2003), 71–87 | MR | Zbl
[3] G. Shafer, V. Vovk, Probability and Finance. It's Only a Game!, Wiley, Chichester, 2001 | MR | Zbl
[4] D. A. Molodtsov, Teoriya myagkikh mnozhestv, URRS, M., 2004
[5] B. de Finetti, Theory of Probability, Wiley, N.Y., 1990 | MR | Zbl
[6] V. P. Maslov, V. P. Myasnikov, V. G. Danilov, Matematicheskoe modelirovanie avariinogo bloka Chernobylskoi AES, Nauka, M., 1987 | MR | Zbl
[7] A. N. Kolmogorov, Yubileinoe izdanie k 100-letiyu A. N. Kolmogorova. V trekh knigakh. Kniga vtoraya, Fizmatlit, M., 2003 | MR | Zbl
[8] R. E. Paierls, Zakony prirody, Fizmatgiz, M., 1962
[9] R. Kubo, Termodinamika, Mir, M., 1970
[10] L. L. Landau, E. M. Lifshits, Kvantovaya mekhanika, Gostekhizdat, M., 1948 | MR | Zbl
[11] N. N. Bogolyubov, Izv. AN SSSR. Ser. fiz., 11:1 (1947), 77–90 | MR
[12] N. N. Bogolyubov, Izbrannye trudy. V trekh tomakh, t. 1, 2, Naukova dumka, Kiev, 1970 | MR
[13] V. M. Long, Maslov-type index, degenerate critical points, and asymptotically linear hamiltonian systems, Science Press, Beijing, 1990 | MR | Zbl
[14] K. Hongo, Yu. Ji, Radio Science, 22 (1987), 357–366 | DOI
[15] V. P. Maslov, Matem. zametki, 80:6 (2006), 856–863 | DOI | MR | Zbl
[16] V. P. Maslov, Matem. zametki, 78:6 (2005), 870–877 | DOI | MR | Zbl
[17] V. P. Maslov, Matem. zametki, 78:3 (2005), 377–395 | DOI | MR | Zbl
[18] V. P. Maslov, Matem. zametki, 80:2 (2006), 220–230 | DOI | MR | Zbl
[19] \Hrefs M. V. Fedoryuk, Metod perevala, Nauka, M., 1977 | MR | Zbl
[20] G. V. Koval, Chastnoe soobschenie, 2006
[21] M. Gromov, Asymptotic invariants of infinite groups. Geometric Group Theory, vol. 2, Cambridge University Press, 1993 | MR | Zbl
[22] L. D. Landau, E. M. Livshits, Statisticheskaya fizika, Nauka, M., 1976 | MR | Zbl
[23] V. P. Maslov, T. V. Maslova, Matem. zametki, 80:5 (2006), 718–732 | DOI | MR | Zbl
[24] R. V. Goldshtein, A. B. Mosolov, PMM, 56:4 (1992), 663–671 ; Докл. РАН, 329:4 (1993), 429–431 | MR | Zbl
[25] B. Mandelbrot, Fraktalnaya geometriya prirody, Institut kompyuternykh issledovanii, M., 2002 | MR | Zbl
[26] V. P. Maslov, P. P. Mosolov, Izv. AN SSSR. Ser. matem., 42:5 (1978), 1063–1100 ; В. П. Маслов, Квантование термодинамики и ультравторичное квантование, Институт компьютерных исследований, М., 2001 | MR | Zbl
[27] R. H. Dauskardt, F. Haubensak, R. O. Ritchie, Acta Metallurgica et Materialia, 38 (1990), 143–159 | DOI
[28] V. P. Maslov, P. P. Mosolov, Nonlinear wave equations perturbed by viscous terms, Walter de Gruyter, Berlin, N. Y., 2000 | MR | Zbl