Airy distribution: Experiment, large deviations, and additional statistics

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number013174
JournalPhysical Review Research
Issue number1
StatePublished - Feb 2020


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