4 problems

Hydrodynamic-limit conjecture. The hydrodynamic limit is given by a diffusion equation with diffusion coefficient $D_\infty$.

Hamiltonian structure conjecture. There exist an energy $\mathcal{E}:\mathcal{Z}\to\mathbb{R}$ and a skew-symmetric operator…

MFT slow-relaxation-mode conjecture. The non-optimal extremisers of the MFT action are the slow relaxation modes of the system.

MFT extremal-profile conjecture. All non-optimal extremal profiles obtained from the MFT are excited states of the biased open ASEP, unless $bc=0$, in which case they are excited s…