LAPLACE-TYPE EXACT ASYMPTOTIC FORMULAS FOR THE BOGOLIUBOV GAUSSIAN MEASURE

We obtain new asymptotic formulas for two classes of Laplace-type functional integrals with the Bogoliubov measure. The principal functionals are the L-p functionals with 0 < p < infinity and two functionals of the exact-upper-bound type. In particular, we prove theorems on the Laplace-type asymptotic behavior for the moments of the L-p norm of the Bogoliubov Gaussian process when the moment order becomes infinitely large. We establish the existence of the threshold value p(0) = 2 + 4 pi(2)/beta(2)omega(2), where beta > 0 is the inverse temperature and omega > 0 is the harmonic oscillator eigenfrequency. We prove that the asymptotic behavior under investigation differs for 0 < p < p(0) and p > p(0). We obtain similar asymptotic results for large deviations for the Bogoliubov measure. We establish the scaling property of the Bogoliubov process, which allows reducing the number of independent parameters.