Geometrical optics of large deviations of Brownian motion in inhomogeneous media

Tal Bar, Baruch Meerson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Geometrical optics provides an instructive insight into Brownian motion, ‘pushed’ into a large-deviations regime by imposed constraints. Here we extend geometrical optics of Brownian motion by accounting for diffusion inhomogeneity in space. We consider three simple model problems of Brownian motion on the line or in the plane in situations where the diffusivity of the Brownian particle depends on one spatial coordinate. One of our results describes ‘Brownian refraction’: an analog of refraction of light passing through a boundary between two media with different refraction indices.

Original languageAmerican English
Article number093301
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number9
StatePublished - 1 Sep 2023

Bibliographical note

Funding Information:
We thank Oded Farago for useful comments. B M was supported by the Israel Science Foundation (Grant No. 1499/20).

Publisher Copyright:
© 2023 The Author(s). Published on behalf of SISSA Medialab srl by IOP Publishing Ltd.


  • Brownian motion [100]
  • fluctuation phenomena [75]
  • large deviations in non-equilibriumsystems [100]


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