Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure

DOI10.1007/s11232-011-0092-0zbMath1297.46057OpenAlexW2161206516MaRDI QIDQ378540

V. R. Fatalov

Publication date: 12 November 2013

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-011-0092-0

zbMATH Keywords

large deviation principleaction functionalBogoliubov measureLaplace method in Banach space

Mathematics Subject Classification ID

Feynman diagrams (81T18) Path integrals in quantum mechanics (81S40) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds (46T12)

Related Items (6)

Exact Laplace-type asymptotic formulas for the Bogoliubov Gaussian measure: the set of minimum points of the action functional ⋮ Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the \(L^{p}\) norm, \(2 \leq p \leq \infty\) ⋮ Perturbation theory series in quantum mechanics: phase transition and exact asymptotic forms for the expansion coefficients ⋮ The Laplace method for Gaussian measures and integrals in Banach spaces ⋮ Functional integrals for the Bogoliubov Gaussian measure: exact asymptotic forms ⋮ Gaussian Ornstein-Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for \( L^{p}\)-functionals, \(0<p<\infty\)

Cites Work

• Asymptotic approximations for probability integrals
• Small deviations for two classes of Gaussian stationary processes and \(L^p\)-functionals, \(0<p\leq\infty\)
• Asymptotic analysis of Gaussian integrals. II: Manifold of minimum points
• Entropy, large deviations, and statistical mechanics.
• Differential equation for a functional integral
• Some asymptotic formulas for the Bogoliubov Gaussian measure
• Gaussian measures in Banach spaces
• Gaussian functional integrals and Gibbs equilibrium averages
• Exact asymptotics of large deviations of stationary Ornstein-Uhlenbeck processes for \(L^p\)-functionals, \(p>0\)
• Negative-order moments for $ L^p$-functionals of Wiener processes: exact asymptotics
• Large Deviations and Metastability
• Exact asymptotics of Laplace-type Wiener integrals for $ L^p$-functionals
• The Laplace method for probability measures in Banach spaces
• Letter to the Editors
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Asymptotic probabilities and differential equations
• ON EIGENFUNCTIONS OF AN OPERATOR CORRESPONDING TO THE POLES OF THE ANALYTIC CONTINUATION OF THE RESOLVENT THROUGH THE CONTINUOUS SPECTRUM
• Large deviations
• Some properties of functional integrals with respect to the Bogoliubov measure
• Metric properties of Bogoliubov trajectories in statistical equilibrium theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure