Gibbs measures relative to Brownian motion

DOI10.1214/aop/1022677444zbMath0965.60095OpenAlexW2046112471MaRDI QIDQ1568283

Herbert Spohn, Hirofumi Osada

Publication date: 25 July 2001

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1022677444

zbMATH Keywords

Brownian motionGibbs measurespair potential

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21)

Related Items (14)

Euclidean Gibbs measures on loop lattices: existence and a priori estimates. ⋮ Existence and a priori estimates for Euclidean Gibbs states ⋮ Gibbs states of interacting systems of quantum anharmonic oscillators ⋮ Central limit theorem for Gibbs measures on path spaces including long range and singular interactions and homogenization of the stochastic heat equation ⋮ A phase transition in a quenched amorphous ferromagnet ⋮ Reciprocal processes. A measure-theoretical point of view ⋮ Functional integral approach to semi-relativistic Pauli-Fierz models ⋮ Tightness and Line Ensembles for Brownian Polymers Under Geometric Area Tilts ⋮ Strong convergence to the homogenized limit of elliptic equations with random coefficients ⋮ DIFFUSION PROCESSES ON PATH SPACES WITH INTERACTIONS ⋮ Construction of Gibbs measures for 1-dimensional continuum fields ⋮ Euclidean Gibbs measures of interacting quantum anharmonic oscillators ⋮ Some penalisations of the Wiener measure ⋮ Decay of correlations in multicomponent ferromagnets with long-range interaction

Cites Work

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• The phase transition in the one-dimensional Ising model with \(1/r^2\) interaction energy
• Gibbs measures and phase transitions
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• Superstable interactions in classical statistical mechanics
• On the absence of phase transition in one-dimensional random fields

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