10 problems

Maximal-current mixing-time conjecture. Theorem 1 remains valid in the maximal current phase for general $A,C\leq 1$.

Quadratic mixing-time conjecture. The correct order of the mixing time in Theorem 2 is $N^2$.

Maximal-current current-variance conjecture. Lemma 1 extends to the entire maximal current phase of the open ASEP.

Consider the open ASEP with light particles at the triple point $(A,C)=(1,1)$, and let $r=1$. Write $\mathbf{loc}_1$ for the location of the single light particle in a system of si…

Let $A$, $C$, and $r$ be the parameters of the open ASEP with light particles, and let $AC\leq 1$ be the fan-region condition in Theorem. The stationary measure of the standard ope…

Let $H_{u,v}(t,x)$ denote the Hopf--Cole solution to the open KPZ equation with Neumann boundary parameters $u$ and $v$, and set … Let $h_{u,v,w,r}^{(N)}(t,x)$ be the diffusively s…

Consider the open ASEP and its height-function process under the weak asymmetry and height-function scaling assumptions used in the paper, with boundary parameters satisfying the s…

Let the open ASEP height function process be defined with ASEP parameters, and let Liggett's condition denote the parameter restriction used in existing convergence results for the…

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…