Enlargement of obstacles for the simple random walk (Q1902942)

Consider a continuous-time simple random walk moving among obstacles, which are either sites of the lattice \(\mathbb{Z}^d\), \(d \geq 1\), or bonds. In this context there is developed a version of the technique of enlargement of obstacles devised in the Brownian case by \textit{A.-S. Sznitman} [J. Funct. Anal. 94, No. 2, 223-246 (1990; Zbl 0732.60088), ibid. 94, No. 2, 247-272 (1990; Zbl 0732.60089) and Ann. Probab. 21, No. 1, 490-508 (1993; Zbl 0769.60104)]. The method gives control on exponential moments of certain death times as well as good lower bounds for certain principal eigenvalues. An application is given to the number of bonds visited by the random walk. As another application an asymptotic result of \textit{M. D. Donsker} and \textit{S. R. S. Varadhan} [Commun. Pure Appl. Math. 32, 721-747 (1979; Zbl 0418.60074)] on the number of sites visited by the random walk is derived.