Laplace approximations for sums of independent random vectors. II: Degenerate maxima and manifolds of maxima

DOI10.1007/BF00319983zbMath0608.60018OpenAlexW3091777984MaRDI QIDQ1085870

Erwin Bolthausen

Publication date: 1987

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00319983

zbMATH Keywords

entropy functionLaplace approximationsdegenerate maximamanifolds of maxima

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Related Items (13)

Multiple critical behavior of probabilistic limit theorems in the neighborhood of a tricritical point ⋮ The scaling limit for a stochastic PDE and the separation of phases ⋮ Sharp asymptotics of large deviations in \(\mathbb{R}^ d\) ⋮ A large deviation principle for \(m\)-variate von Mises-statistics and \(U\)- statistics ⋮ Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation ⋮ Refinements of the Gibbs conditioning principle ⋮ A Brief Introduction to Large Deviations Theory ⋮ Applications of Stein's method for concentration inequalities ⋮ Large deviations and the internal fluctuations of critical mean field systems ⋮ Large deviations for the empirical field of curie-weiss models^∗ ⋮ Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables ⋮ Asymptotic expansions for ornstein-uhlenbeck semigroups perturbed by potentials over banach spaces ⋮ Critical fluctuations for quantum mean-field models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large deviations of the sample mean in general vector spaces
• On Edgeworth expansions in Banach spaces
• Dominating points and the asymptotics of large deviations for random walk on \(R^ r\).
• Gaussian measures in Banach spaces
• I-divergence geometry of probability distributions and minimization problems
• Upper bounds for large deviations of dependent random vectors
• Asymptotic Analysis of Gaussian Integrals. I. Isolated Minimum Points
• A Laplace approximation for sums of independent random variables
• Gaussian radon measures on locally convex spaces.
• Asymptotic evaluation of certain Markov process expectations for large time—III
• Limit theorems for sums of dependent random variables occurring in statistical mechanics
• Convergence of moments and related functional in the general central limit theorem in banach spaces
• Large deviations from the mckean-vlasov limit for weakly interacting diffusions
• Laplace approximations for sums of independent random vectors

This page was built for publication: Laplace approximations for sums of independent random vectors. II: Degenerate maxima and manifolds of maxima