17 problems

Particle-conjugation symmetry conjecture. The following equality holds:

Let $K_1$ be the product of the first three matrices in the displayed factorization of the TASEP kernel, and let $K_2$ be the operator defined by … Here the operators act on the in…

Orthogonality conjecture. In the limit $c\to\infty$,

Tableau-process weight conjecture. This weight is proportional to the weight derived from the tableau process of Ayyer et al.

In the setting of the section, consider right Bernoulli TASEP with sequential updates and an additional caterpillar of length $b\varepsilon^{-1/2}$ placed at distance…

Let $T_0,\dots,T_{n-1}$ be the absorption times in the type $B$ oriented swap process, and let $L((0,0),(u,v))$ denote the corresponding half-space LPP passage time. Type B distrib…

Let $\alpha>0$, $u>-\alpha$, and let $z_{u,v}$ be the explicitly constructed stationary processes indexed by $v\in(-\alpha,\min(u,0)]$ for the half-space log-gamma polymer. For ini…

Let $E$ be the underlying space, let $\mathbb{P}$ be a point process on $E$, and let $\rho^R$ be an $L^1$-specialization. The pair $(\mathbb{P},\rho^R)$ is Giambelli compatible whe…

Spin Whittaker orthogonality conjecture. For all $\underline{L}_N,\underline{L}'_Ninmathpzc{W}_N$,

Let $\mathbf{U}_N=(U_N(1),\dots,U_N(N-1))$ be the vector of swap-passage times in the oriented swap process, and let $\mathbf{V}_N=(V_N(1),\dots,V_N(N-1))$ be the vector of last-pa…

Fix $t>0$, $\Delta>0$, two segments $[X,X']$ and $[Y,Y']$ in $\mathbb R$, and real numbers $(x_1,\dots,x_n)$, $(y_1,\dots,y_n)$, $(\tilde x_1,\dots,\tilde x_k)$, and…

The q-Hahn PushTASEP Fredholm determinant conjecture. For the step initial configuration,

Existence and uniqueness conjecture. There exists a unique composition $\nu$ for which this specialization is well defined and

Let $\alpha>-1$, let $x,y\in\mathbb{R}_+$ be fixed, and let $\tau\in\mathbb{R}$ be fixed. The function $K^{\operatorname{tac},(\alpha)}(x,y;s,\tau)$ is the hard-edge tacnode kernel…

Let $\boldsymbol\tau$ and $\boldsymbol\nu$ be the model parameters, let $\psi_{\bf w}(\boldsymbol\tau,\boldsymbol\nu)$ denote the component associated with a particle configuration…

Let $q$ satisfy $0<q<1$, let $x_n(t)$ denote the position of particle $n$ at time $t$, and define … For all $\zeta\in\mathbb{C}\setminus\mathbb{R}_{>0}$, the conjectural Fredholm d…

The quintic kernel is defined by … where the $z$- and $\tilde z$-integration paths are appropriate subpaths of the paths shown in the source figure, with the indicated orientation.…