EXACT LAPLACE-TYPE ASYMPTOTIC FORMULAS FOR THE BOGOLIUBOV GAUSSIAN MEASURE: THE SET OF MINIMUM POINTS OF THE ACTION FUNCTIONAL

摘要

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.