Uniqueness and Markovianity of subsequential directed-landscape dynamics

Determine whether the subsequential limiting dynamics on the directed landscape are unique and whether they possess the Markov property.

Background

The paper constructs continuous, stationary, reversible subsequential scaling limits of dynamical Brownian last passage percolation under Ornstein–Uhlenbeck evolution. The construction establishes that every fixed-time marginal is a directed landscape and that the limiting process is nontrivial in dynamical time, but it does not identify a unique law for the full dynamical process.

The authors explicitly leave unresolved whether different subsequences can yield different limiting dynamics and whether the resulting process is Markov. Establishing these properties would give a more canonical and structurally characterized continuum dynamics.

References

Several questions about these subsequential limiting dynamics remain open. Are the subsequential limits unique, and are they Markov? Neither of these properties is established here.

— A non-trivial dynamics on the directed landscape  (2609.35124 - Bhatia, 28 Sep 2026) in Section 1, Introduction, paragraph beginning “Several questions about these subsequential limiting dynamics remain open”