5 problems

Consider the open ASEP with boundary parameters. In the three-parameter case, the basic weight function is described using bi-colored Motzkin paths, while general boundary paramete…

Let the open WASEP have parameters $u$ and $v$, and let $I=\lsem a,b \rsem$ satisfy … For $q$ from the paper's weak-asymmetry assumption with $\varepsilon>0$, consider the low-dens…

Positivity and term count conjecture. The partition function $Z_n=Z_n(\alpha,\beta,q)$ is a positive polynomial with $(n-1)!$ terms, counted with multiplicity.

Let $T(\lambda)$ be the transfer matrix acting on a sector $V(m)$, let $d=\dim V(m)$, and suppose that $p\neq q$ are generic. Eigen-polynomial conjecture. For any sector $V(m)$, in…

Let $m=(m_1,\,\ldots,m_n)\in\mathcal M$ be a sector, let ${\rm Spec}(m)$ denote the spectrum in that sector, and let $E_j^{\pm}(m)=E^{\pm}(m_1+\cdots+m_j,m_{j+1}+\cdots+m_n)$ for…