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

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.