Classical-limit conjecture for multiple chordal SLE(0) partition functions

Let $\mathcal{Z}_{\alpha}(\boldsymbol{z},u)$ and $\mathcal{Z}_{\alpha}(\boldsymbol{x})$ be pure partition functions, and let $\Phi(\boldsymbol{x},\boldsymbol{\xi},u)$ and $\Phi(\boldsymbol{x},\boldsymbol{\xi})$ denote the corresponding multiple chordal SLE(0) master functions. In the first case, $\boldsymbol{\xi}$ is a critical point of $\Phi(\boldsymbol{x},\boldsymbol{\xi},u)$; in the second, it is a critical point of $\Phi(\boldsymbol{x},\boldsymbol{\xi})$. Classical-limit conjecture. As $\kappa\rightarrow0$, the normalized pure partition functions have limits concentrated on critical points of the relevant master function, namely

$$\underset{\kappa\rightarrow0}{\lim}\mathcal{Z}_{\alpha}(\boldsymbol{z})^{\kappa}=\Phi(\boldsymbol{x},\boldsymbol{\xi},u)$$

and, in the special case $u=\infty$,

$$\underset{\kappa\rightarrow0}{\lim}\mathcal{Z}_{\alpha}(\boldsymbol{x})^{\kappa}=\Phi(\boldsymbol{x},\boldsymbol{\xi}).$$

Here $\boldsymbol{\xi}$ is a critical point of the corresponding master function. This conjecture formalizes the heuristic steepest-descent passage from multiple chordal SLE($\kappa$) partition functions to the deterministic multiple chordal SLE(0) system. The existence and concentration of these limits are not established in the supplied text.