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.
We thank J. Baik and Z. Liu for pointing out the missing \(\sqrt{2}\) on the right-hand side of this equality in an earlier version of this manuscript. See [ 10 ] for more details.
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Quastel, J., Remenik, D. (2014). Airy Processes and Variational Problems. In: Ramírez, A., Ben Arous, G., Ferrari, P., Newman, C., Sidoravicius, V., Vares, M. (eds) Topics in Percolative and Disordered Systems. Springer Proceedings in Mathematics & Statistics, vol 69. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0339-9_5
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