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 Button Covers 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 Bearing Grease 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.