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Theoretical and Mathematical Physics

, Volume 191, Issue 3, pp 870–885 | Cite as

Exact Laplace-type asymptotic formulas for the Bogoliubov Gaussian measure: The set of minimum points of the action functional

Article

Abstract

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+4π 2/β 2 ω 2 is a threshold value, β > 0 is the inverse temperature, and ω > 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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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussia

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