Department of Mathematics

Analysis and PDE

  •  Konstantin Matetski, MSU
  •  Polynuclear growth and the Toda lattice
  •  10/05/2022
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall
  •  Willie Wai-Yeung Wong (wongwil2@msu.edu)

Polynuclear growth is one of the basic models in the Kardar-Parisi-Zhang universality class, which describes a one-dimensional crystal growth. For a particular initial state, it describes the length of the longest increasing subsequence for uniformly random permutations (the problem first studied by S. Ulam). In my joint work with J. Quastel and D. Remenik we expressed the distribution functions of the polynuclear growth in terms of the solutions of the Toda lattice, one of the classical integrable systems. A suitable rescaling of the model yields a non-trivial continuous limit of the polynuclear growth (the KPZ fixed point) and the respective equations (Kadomtsev-Petviashvili).

 

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Department of Mathematics
Michigan State University
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C212 Wells Hall
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