Chase-escape percolation is a variation of the standard epidemic spread models. In this model, each site can be in one three states: unoccupied, occupied by single prey, or predator. Prey particles to neighboring empty sites at rate $p$, and predator only prey $1$, killing particle that existed site. It was found survive with non-zero probability, if $p>p_c$ $p_c<1$. Using Monte Carlo simulatio...

In the past decade, a lot of attention has been devoted to the enumeration of walks with prescribed steps confined to a convex cone. In two dimensions, this means counting walks in the first quadrant of the plane (possibly after a linear transformation). But what about walks in non-convex cones? We investigate the two most natural cases: first, square lattice walks avoiding the negative quadran...