3 problems

Consider a general configuration model with a power-law degree sequence, and let $t_{\text{mix}}$ denote its mixing time. Polylogarithmic mixing-time conjecture. The known mixing r…

Let the underlying geometry be modelled by a degree-two configuration model with rewiring, and let ISRW denote the associated random walk. Sublinear-mixing conjecture. ISRW should…

Let $T^N_{\mathrm{MRND}}$ and $T^N_{\mathrm{NSWND}}$ be the final epidemic sizes without dropping of edges on MR and NSW configuration-model random graphs with $N$ vertices. Let…