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The maximal point of the Airy2 process minus a parabola is believed to describe the scaling limit of the end-point of the directed polymer in a random medium, which was proved to be true for a few specific cases.
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2006
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J. Baik, Painlevé formulas of the limiting distributions for non-null complex sample covariance matrices
2006
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C. Tracy, H. Widom, Nonintersecting Brownian excursions
2007
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A. Borodin, P. Ferrari, Large time asymptotics of growth models on space-like paths. I. PushASEP
2008
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A. Borodin, P. Ferrari, T. Sasamoto, Large time asymptotics of growth models on space-like paths. II. PNG and parallel TASEP
2008
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G. Schehr, S. N. Majumdar, A. Comtet, J. Randon-Furling, Exact distribution of the maximal height of p vicious walkers
2008
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L. Petrov, Asymptotics of random lozenge tilings via Gelfand-Tsetlin schemes
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2011
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K. Liechty, Nonintersecting Brownian excursions on the half-line and discrete Gaussian orthogonal polynomials
2012
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T. Feierl, The height of watermelons with wall
2012
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P. Le Doussal, P. Calabrese, The KPZ equation with flat initial condition and the directed polymer with one free end
2012
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K. A. Takeuchi, M. Sano, Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
2012
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