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7. KPZ line ensemble and random permutations


    1. Add remark

      Problem 7.1.

      Take a vertical slice of the KPZ line ensemble [MR3547737], how close is the permutation of $\mathbb{Z}_{\ge1}$ to the identity permutation? Is the permutation finite at all? In the Airy line ensemble, the permutation is trivial with probability 1.

      Note that there are two versions of the KPZ line ensemble: the one where the $k$-th curve escapes to $+\infty$ (when the Gibbs property is independent of $k$), and the one where the deep curves stabilize (but the Gibbs property depends on $k$; this second version is the one arising as scaling limits).

          Cite this as: AimPL: All roads to the KPZ universality class, available at http://aimpl.org/roadtokpz.