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Airy Processes and Variational Problems

  • Jeremy QuastelEmail author
  • Daniel Remenik
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 69)

Abstract

We review the Airy processes—their formulation and how they are conjectured to govern the large time, large distance spatial fluctuations of 1-D random growth models. We also describe formulae 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 formulae to variational problems involving Airy processes that arise in physical problems, as well as to their local behaviour.

Keywords

Fredholm Determinant Stochastic Heat Equation Gaussian Unitary Ensemble Gaussian Orthogonal Ensemble Airy Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Departamento de Ingenieria Matemática and Centro de Modelamiento MatemáticoUniversidad de ChileSantiagoChile

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