Place an obstacle with probability 1-p 1-p independently at each vertex of Z^ d Z d, and run
a simple random walk before hitting one of the obstacles. For d ≥ 2 d≥ 2 and p strictly …

We consider a random walk among a Poisson cloud of moving traps on ${\mathbb Z}^ d $,
where the walk is killed at a rate proportional to the number of traps occupying the same …

We consider a one-dimensional simple random walk killed by quenched soft obstacles. The
position of the obstacles is drawn according to a renewal process with a power-law …

We consider the Dirichlet eigenvalues of the Laplacian among a Poissonian cloud of hard
spherical obstacles of fixed radius in large boxes of R d, d≥ 2. In a large box of side-length …

In this article, we study a discrete version of a Dirichlet problem in an open bounded set $
D\subset\mathbb {R}^ d $, in dimension $ d\geq 2$. More precisely, we consider the simple …

In this paper we consider the simple random walk on $\mathbb {Z}^ d $, $ d\geq 3$,
conditioned to stay in a large domain $ D_N $ of typical diameter $ N $. Considering the …

We investigate a model of continuous-time simple random walk paths in $\mathbb {Z}^ d $
undergoing two competing interactions: an attractive one towards the large values of a …

The random walk among Bernoulli obstacles model describes a system in which particles
move randomly in a space containing random traps. More precisely, obstacles are placed …