Exact Laplace-type asymptotic formulas for the~Bogoliubov Gaussian measure: The~set of minimum points of the~action functional
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 456-472
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We prove a theorem on the exact asymptotic relations of large deviations of the Bogoliubov measure in the $L^p$ norm for $p=4,6,8,10$ with $p>p_0$, where $p_0=2+4\pi^2/\beta^2\omega^2$ is a threshold value, $\beta>0$ is the inverse temperature, and $\omega>0$ is the natural frequency of the harmonic oscillator. For the study, we use the Laplace method in function spaces for Gaussian measures.
Keywords:
Bogoliubov measure, Laplace method in a Banach space, action functional, set of minimum points.
@article{TMF_2017_191_3_a6,
author = {V. R. Fatalov},
title = {Exact {Laplace-type} asymptotic formulas for {the~Bogoliubov} {Gaussian} measure: {The~set} of minimum points of the~action functional},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {456--472},
publisher = {mathdoc},
volume = {191},
number = {3},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a6/}
}
TY - JOUR AU - V. R. Fatalov TI - Exact Laplace-type asymptotic formulas for the~Bogoliubov Gaussian measure: The~set of minimum points of the~action functional JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2017 SP - 456 EP - 472 VL - 191 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a6/ LA - ru ID - TMF_2017_191_3_a6 ER -
%0 Journal Article %A V. R. Fatalov %T Exact Laplace-type asymptotic formulas for the~Bogoliubov Gaussian measure: The~set of minimum points of the~action functional %J Teoretičeskaâ i matematičeskaâ fizika %D 2017 %P 456-472 %V 191 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a6/ %G ru %F TMF_2017_191_3_a6
V. R. Fatalov. Exact Laplace-type asymptotic formulas for the~Bogoliubov Gaussian measure: The~set of minimum points of the~action functional. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 456-472. http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a6/