| Title:
|
The principle of the largest terms and quantum large deviations (English) |
| Author:
|
Gulinsky, Oleg V. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
[229]-247 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give an approach to large deviation type asymptotic problems without evident probabilistic representation behind. An example provided by the mean field models of quantum statistical mechanics is considered. (English) |
| Keyword:
|
idempotentmeasures |
| Keyword:
|
quantum large deviations |
| MSC:
|
06F05 |
| MSC:
|
81S05 |
| MSC:
|
82B10 |
| MSC:
|
93B27 |
| MSC:
|
93C65 |
| MSC:
|
93E03 |
| idZBL:
|
Zbl 1249.93156 |
| idMR:
|
MR1996560 |
| . |
| Date available:
|
2009-09-24T19:53:07Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135524 |
| . |
| Reference:
|
[1] Bourbaki N.: Intégration, Chap.6. Hermann, Paris 1959 Zbl 0213.07501, MR 0124722 |
| Reference:
|
[2] Breyer V., Gulinsky O.: Large deviations on infinite dimentional spaces (in Russian).Preprint of MIPT, Moscow 1996 |
| Reference:
|
[3] Bryc W.: Large deviations by the asymptotic value method.In: Diffusion Processes and Related Problems in Analysis (M. Pinski, ed.), Birkhäuser, Boston 1990, pp. 447–472 Zbl 0724.60032, MR 1110177 |
| Reference:
|
[4] Choquet G.: Theory of capacities.Ann. Inst. Fourier 5 (1955), 131–295 MR 0080760, 10.5802/aif.53 |
| Reference:
|
[5] Davies E. B., Simon B.: Ultracontractivity and the heat kernal for Schrödinger operators and Dirichlet laplacians.J. Funct. Anal. 59 (1984), 335–395 MR 0766493, 10.1016/0022-1236(84)90076-4 |
| Reference:
|
[6] Kolokoltsov V. N., Maslov V. P.: The general form of the endomorphisms in the space of continuous functions with values in a numerical semiring with the operation $\oplus =\max $.Soviet Math. Dokl. 36 (1988), 1, 55–59 MR 0902683 |
| Reference:
|
[7] Minlos R. A., Verbeure, A., Zagrebnov V.: A quantum crystal model in the light-mass limit: Gibbs state.Rev. Math. Phys. 12 (2000), 981–1032 MR 1782692, 10.1142/S0129055X00000381 |
| Reference:
|
[9] Puhalskii A.: Large deviations of semimartingales via convergence of the predictable characteristics.Stochastics 49 (1994), 27–85 Zbl 0827.60017, MR 1784438 |
| Reference:
|
[10] Puhalskii A.: The method of stochastic exponentials for large deviations.Stochastic Process. Appl. 54 (1994), 45–70 MR 1302694 |
| . |
