Occupation-time statistics of a gas of interacting diffusing particles

Tal Agranov, P. L. Krapivsky, Baruch Meerson

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10 Scopus citations


The time that a diffusing particle spends in a certain region of space is known as the occupation time, or the residence time. Recently, the joint occupation-time statistics of an ensemble of noninteracting particles was addressed using the single-particle statistics. Here we employ the macroscopic fluctuation theory (MFT) to study the occupation-time statistics of many interacting particles. We find that interactions can significantly change the statistics and, in some models, even cause a singularity of the large-deviation function describing these statistics. This singularity can be interpreted as a dynamical phase transition. We also point out to a close relation between the MFT description of the occupation-time statistics of noninteracting particles and the level 2 large deviation formalism which describes the occupation-time statistics of a single particle.

Original languageAmerican English
Article number052102
JournalPhysical Review E
Issue number5
StatePublished - 2 May 2019

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© 2019 American Physical Society.


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