Abstract
We consider an interacting particle system driven by a Hamiltonian dynamics and perturbed by a conservative stochastic noise so that the full system conserves two quantities: energy and volume. The Hamiltonian part is regulated by a scaling parameter vanishing in the limit. We study the form of the fluctuations of these quantities at equilibrium and derive coupled stochastic partial differential equations with a KPZ flavor.
Nous considérons un système de particules en interaction régi par une dynamique hamiltonienne perturbée par un bruit stochastique conservatif de sorte que le système complet conserve deux quantités : l’énergie et le volume. La partie hamiltonienne est régulée par un paramètre d’échelle disparaissant à la limite. Nous étudions la forme des fluctuations de ces quantités à l’équilibre et dérivons des équations aux dérivées partielles stochastiques couplées qui ont une fragrance de KPZ.
Acknowledgements
This work has been supported by the projects EDNHS ANR-14- CE25-0011, LSD ANR-15-CE40-0020-01 of the French National Research Agency (ANR). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement No 715734). The work of M.S. was also partly supported by the Labex CEMPI (ANR-11-LABX-0007-01) and the project MICMOV ANR-19-CE40-0012. We thank Günter Schütz for his interest in this work.
Citation
Ragaa Ahmed. Cédric Bernardin. Patrícia Gonçalves. Marielle Simon. "A microscopic derivation of coupled SPDE’s with a KPZ flavor." Ann. Inst. H. Poincaré Probab. Statist. 58 (2) 890 - 915, May 2022. https://doi.org/10.1214/21-AIHP1196
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