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

Abstract

We prove a theorem on the exact asymptotic relations of large deviations of the Bogoliubov measure in the L^pnorm for p = 4, 6, 8, 10 with p > p₀, where p₀ = 2+4π²/β²ω²is 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.