Some examples of translation invariant site percolation processes on the $Z^2$ lattice are constructed, the most far-reaching example being one that satisfies uniform finite energy (meaning that the probability that a site is open given the status of all others…

For two-dimensional last-passage time models of weakly increasing paths, interesting scaling limits have been proved for points close the axis (the hard edge). For strictly increasing paths of Bernoulli($p$) marked sites, the relevant boundary is the line $y=px$. We call…

We investigate dual mechanisms for interacting particle systems. Generalizing an approach of Alkemper and Hutzenthaler in the case of coalescing duals, we show that a simple linear transformation leads to a moment duality of suitably rescaled processes. More precisely, we…

Consider critical bond percolation on a large $2 n \times 2 n$ box on the square lattice. It is well-known that the size (i.e. number of vertices) of the largest open cluster is, with high probability, of order $n^2 \pi(n)$, where $\pi(n)$ denotes…