3 problems

Let $s\in\mathbb{S}^{d-1}$, let $n$ tend to infinity, let $\beta_{\rm sat}^{*}(s)$ be the saturation threshold for the truncated two-point function, let $\beta_{\rm c}$ be the crit…

Let $\beta_{\rm sat}(s)$ denote the saturation threshold in direction $s$, and let $\beta_{\rm sat}^{*}(s)$ be the corresponding threshold for the truncated two-point function. Let…

For ${\sf x}\in\mathbb Z^{d+1}$, let ${\mathfrak t}_{\sf x}^\omega$ denote the quenched polymer connectivity function, let ${{\mathbf t}}_{\sf x}$ denote its averaged counterpart,…