KPZ Fixed point

•  Finding a transition probability formula that is amenable to taking limit as the number of TASEP particles goes to infinity. Prize: 50$
  • Is there an analogous backwards heat equation problem as in the KPZ fixed point for Z-TASEP?
• Identifying the KPZ fixed point in the subcritical region Prize: 50$

.

RSK correspondence formula

In “Determinantal transition kernels for some interacting particles on the line” Dieker and Warren derive the transition probability formula for various particle processes on the infinite line. For example, they rederived Schutz’s formula for Z-TASEP. Can the Baik-Liu formula be rederived in the same spirit of techniques.

• What will be the periodic Gelfand-Tsetlin and Young Tableaus that are in bijection with the dynamics of periodic TASEP? Prize: 50$