Abstract
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 language | English |
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Article number | 013174 |
Journal | Physical Review Research |
Volume | 2 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2020 |
Bibliographical note
Publisher Copyright:© 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.