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arXiv · 1301.0750

Airy processes and variational problems

Jeremy Quastel·Daniel Remenik
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Abstract

We review the Airy processes; their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of one dimensional random growth models. We also describe formulas which express the probabilities that they lie below a given curve as Fredholm determinants of certain boundary value operators, and the several applications of these formulas to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.

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Jeremy Quastel, Daniel Remenik. 2013-01-04. Airy processes and variational problems. https://doi.org/10.1007/978-1-4939-0339-9_5

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