The principle of the largest terms and quantum large deviations
Kybernetika, Tome 39 (2003) no. 2, pp. 229-247 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 06F05, 81S05, 82B10, 93B27, 93C65, 93E03
Keywords: idempotentmeasures; quantum large deviations
@article{KYB_2003_39_2_a11,
     author = {Gulinsky, Oleg V.},
     title = {The principle of the largest terms and quantum large deviations},
     journal = {Kybernetika},
     pages = {229--247},
     year = {2003},
     volume = {39},
     number = {2},
     mrnumber = {1996560},
     zbl = {1249.93156},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003_39_2_a11/}
}
TY  - JOUR
AU  - Gulinsky, Oleg V.
TI  - The principle of the largest terms and quantum large deviations
JO  - Kybernetika
PY  - 2003
SP  - 229
EP  - 247
VL  - 39
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KYB_2003_39_2_a11/
LA  - en
ID  - KYB_2003_39_2_a11
ER  - 
%0 Journal Article
%A Gulinsky, Oleg V.
%T The principle of the largest terms and quantum large deviations
%J Kybernetika
%D 2003
%P 229-247
%V 39
%N 2
%U http://geodesic.mathdoc.fr/item/KYB_2003_39_2_a11/
%G en
%F KYB_2003_39_2_a11
Gulinsky, Oleg V. The principle of the largest terms and quantum large deviations. Kybernetika, Tome 39 (2003) no. 2, pp. 229-247. http://geodesic.mathdoc.fr/item/KYB_2003_39_2_a11/

[1] Bourbaki N.: Intégration, Chap. 6. Hermann, Paris 1959 | MR | Zbl

[2] Breyer V., Gulinsky O.: Large deviations on infinite dimentional spaces (in Russian). Preprint of MIPT, Moscow 1996

[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 | MR | Zbl

[4] Choquet G.: Theory of capacities. Ann. Inst. Fourier 5 (1955), 131–295 | DOI | MR

[5] Davies E. B., Simon B.: Ultracontractivity and the heat kernal for Schrödinger operators and Dirichlet laplacians. J. Funct. Anal. 59 (1984), 335–395 | DOI | MR

[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

[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 | DOI | MR

[9] Puhalskii A.: Large deviations of semimartingales via convergence of the predictable characteristics. Stochastics 49 (1994), 27–85 | MR | Zbl

[10] Puhalskii A.: The method of stochastic exponentials for large deviations. Stochastic Process. Appl. 54 (1994), 45–70 | MR