3 problems

Let $d=2$ and suppose that Assumption-(i) and the moment condition hold, in particular $\operatorname{\mathbb{P}}[\omega(e)>0]=1$ for $e\in E_d$. For $n\in\mathbb{N}$, set … and ……

Let ${\mathcal K}=\{\mathcal K(x,y):x,y\in\mathbb Z^d,\,x\sim y\}$ be a field of random conductances on neighbouring sites, and let $\lambda_0({\mathcal K})$ denote the associated…

Let $gamma<infty$, and suppose that the conductance parameters $gamma_{k,m}$ are different. Let (ii) denote assertion (ii) of Theoremcomparaspeeds in the source. Comparison-of-spee…