6 problems

Let $\tau$ and $\hat\tau$ be renewal sets with tail exponents … , respectively, and let $h_c(\beta)$ and $h_c^a(\beta)$ denote the quenched and annealed critical points of the pinn…

Let $F(\beta,h)$ be the quenched free energy, let $h_c(\beta)$ be the critical point, and suppose the renewal inter-arrival law satisfies the regular-variation assumption and the e…

Let $\tau$ be the renewal process with inter-arrival law $K$, and let $h_c(\beta)$ denote the critical point at disorder intensity $\beta$. Assume that the environment satisfies th…

Let $h_c(\beta)$ be the critical curve of a disordered pinning model, and let $\boldsymbol h_c^{(\alpha)}(1)$ be the critical curve of the continuum model at unit coupling. For a s…

Cheliotis–den Hollander conjecture. For every $\mu_0$,

Let $\alpha\in(0,\infty)$, let $\chi:=\sum_{n\in\mathbb{N}}[\textbf{P}(S_n=0)]^2$, and let $\beta_c$ denote the critical inverse temperature separating the annealed and quenched cr…