Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
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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/

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