3 problems

Quenched giant-component conjecture. A quenched version of this theorem holds.

Let $d\geq 3$. For $u\geq 0$, let $\mathcal V^u$ denote the vacant set of random interlacements, and let $\mathcal V^{u,\varepsilon}$ denote its $\varepsilon$-disordered version. D…

Derrida–Hakim–Vannimenus disorder relevance conjecture. Disorder is relevant when $1/2<lpha<1$, irrelevant when $lpha<1/2$, and marginally relevant when $lpha=1/2$. More precisely,…