Free energy in a mean field of Brownian particles

DOI10.3934/dcds.2019031zbMath1404.60116OpenAlexW2900243859WikidataQ128951362 ScholiaQ128951362MaRDI QIDQ1757419

Xia Chen, Phan Van Tuoc

Publication date: 4 January 2019

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2019031

zbMATH Keywords

Brownian motionground state energyparabolic Anderson modelmean fieldmany body problemDonskervaradhan large deviationsHartree's theory

Mathematics Subject Classification ID

Brownian motion (60J65) Other physical applications of random processes (60K40) Large deviations (60F10) Many-body theory; quantum Hall effect (81V70) Processes in random environments (60K37) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (5)

Some recent progress on stochastic heat equations ⋮ Parabolic Anderson model with a fractional Gaussian noise that is rough in time ⋮ Precise high moment asymptotics for parabolic Anderson model with log-correlated Gaussian field ⋮ Spatial asymptotic of the stochastic heat equation with compactly supported initial data ⋮ Parabolic Anderson model with rough or critical Gaussian noise

Cites Work

• Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noise
• On the chaotic character of the stochastic heat equation. II
• On the chaotic character of the stochastic heat equation, before the onset of intermitttency
• Stochastic heat equation with rough dependence in space
• Large deviations for Riesz potentials of additive processes
• Exponential asymptotics for time-space Hamiltonians
• Stochastic heat equation driven by fractional noise and local time
• Extending martingale measure stochastic integral with applications to spatially homogeneous S. P. D. E's
• Derivation of Hartree's theory for generic mean-field Bose systems
• The quantum N-body problem
• Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics
• Asymptotic evaluation of certain Markov process expectations for large time—III
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