2 problems

Let $w$ be a nondecreasing weight sequence satisfying … Extend $w$ to the positive reals by $w(t)=w(\lfloor t\rfloor)$, define … and let $W^{-1}$ be its inverse. Set … … and, with…

Let $X$ be a vertex-reinforced non-backtracking random walk on a connected finite undirected graph, with reinforcement function $W(k)=(1+k)^\alpha$. Let $C=\{i_1,\dots,i_\ell\}$ be…