Airy distribution: Experiment, large deviations, and additional statistics

Tal Agranov, Pini Zilber, Naftali R. Smith, Tamir Admon, Yael Roichman, Baruch Meerson

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16 Scopus citations


The Airy distribution (AD) describes the probability distribution of the area under a Brownian excursion. The AD is prominent in several areas of physics, mathematics, and computer science. Here we use a dilute colloidal system to directly measure the AD in experiment. We also show how two different techniques of theory of large deviations, the Donsker-Varadhan formalism and the optimal fluctuation method, manifest themselves in the AD. We advance the theory of the AD by calculating, at large and small areas, the position distribution of a Brownian excursion conditioned on a given area and measure its mean in the experiment. For large areas, we uncover two singularities in the large-deviation function, which can be interpreted as dynamical phase transitions of third order. For small areas the position distribution coincides with the Ferrari-Spohn distribution, and we identify the reason for this coincidence.

Original languageAmerican English
Article number013174
JournalPhysical Review Research
Issue number1
StatePublished - Feb 2020

Bibliographical note

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© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.


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