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2. Multilayer models and multilayer KPZ FP


    1. Add remark

      Problem 2.1.

      There has been success in finding exact formulas for PNG with arbitrary initial conditions [arXiv:2209.02643]. Can this be extended to multilayer PNG? What class of initial conditions can we consider?


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          Problem 2.2.

          Find the scaling limit of the multilayer PNG in the spirit of KPZ FP [MR4346267], [arXiv:2209.02643

          ].


            • Add remark

              Problem 2.3.

              More generally, consider multilayer models such as the multi-path partition functions in the O’Connell-Yor semi-discrete directed Brownian polymer, see Theorem 3.1 and subsequent SDEs in [MR2952082], Definition 4.1.26 in [MR3204480], Section 8.4[MR3534830]. At the edge, this model scales to the KPZ equation and further to the KPZ fixed point. What is the scaling limit in the bulk? Potential related models include Macdonald processes and general beta random matrix ensembles (both dynamical — Dyson Brownian motion — and the corners process). One reference is on the $q$-deformed bulk dynamics [MR3510252].

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