2 problems

Let $f_{\beta}$ be the free-energy random variable, let $G$ be an independent Gumbel random variable, and define … Let $V_m$ denote the minimum of the underlying logarithmically co…

Let $p_{\beta}(x)$ be the Gibbs-measure density in the random landscape, and let $\overline{p_{\beta}(x)}$ denote its disorder average. Write $\mathcal{P}(x)$ for the probability d…