Mixing-time regime for RBPD Markov chains

Establish rigorous mixing-time bounds that resolve whether the Markov chain on reduced bumpless pipe dreams (e.g., with local 2×2 flips and/or droop moves) mixes in polynomial time or exhibits exponential mixing time, thereby proving a polynomial/exponential distinction.

Background

The authors’ experiments suggest that chains augmented with sufficiently large rectangular droop/undroop moves may mix rapidly, whereas flip-only dynamics appear exponentially slow, akin to certain six-vertex regimes.

However, no rigorous bounds are known; proving sharp mixing-time behavior across move sets would clarify algorithmic efficiency and phase behavior.