Large Deviations, Free Energy Functional and Quasi-Potential for a Mean Field Model of Interacting DiffusionsAmerican Mathematical Soc., 1989 - 94 pages Large deviations for an exchangeable system of reversible diffusions in [double-struck]R[superscript italic]d are investigated in the limit when the number of particles tends to infinity with the objective of providing a methodology to study dynamical phase transitions, tunnelling and metastability for the class of mean field models in statistical physics. |
Table des matières
| 1 | |
2 The mean field model Basic notation | 12 |
3 Main results | 18 |
4 Large deviations for the invariant distributions | 27 |
5 Quasipotential and free energy functional for noninteracting systems | 30 |
6 Quasipotential and free energy functional for interacting systems | 50 |
References | 93 |
Expressions et termes fréquents
²au absolutely continuous action functional Applying arbitrarily assertion Assumption Ul belongs C₂ Cameron-Martin-Girsanov formula Co,t Co(IR compact subset conclude const continuous with respect Cs,o Cs,t defined density Department of Mathematics domain of attraction empirical process exists exp{F(x exponential follows free energy functional functional F Gärtner 14 Given Hölder's inequality infimum interacting diffusions interaction-free invariant distribution invariant probability measure IRª law of large limsup lower semicontinuous Markov property martingale martingale problem McKean-Vlasov dynamics McKean-Vlasov equation mean field model measurable function measure-valued trajectories metastability non-negative measurable function norm normalizing constant positive constants probability law probability measure proof of Lemma quasi-transition operators quasipotential Section stationary stochastic supremum time-reversed McKean-Vlasov path topology transition operators u e s,t weak solution Wiener process yields αμ νε Μ