Abstract
The techniques presented in the first part of the book have a wide range of applications. They have been used, for instance, to prove the hydrodynamic limit of non-gradient interacting particle systems. To illustrate this fact, we depart in this chapter from the main stream of the book and consider the fluctuations of a scalar random field instead of the fluctuations of a particle or the fluctuations of an additive functional. In this chapter, we examine the equilibrium space-time fluctuations of the density field of simple exclusion processes. As the dynamics conserve the total number of particles, the fluctuations of the density field evolve in a longer time scale than the other fluctuation fields, yielding to an autonomous equation in a proper scaling limit.
The fluctuation–dissipation theorem, which is the main step in the proof of the fluctuations of the density field, is the subject of this chapter and uses the methods presented in the first part of the book.
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Komorowski, T., Landim, C., Olla, S. (2012). Equilibrium Fluctuations of the Density Field. In: Fluctuations in Markov Processes. Grundlehren der mathematischen Wissenschaften, vol 345. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29880-6_7
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