Abstract: Consider the region $L:= \{(x,y): 0 \leq y \leq C \log(1+x), x > 0\}$ for a constant $C > 0$. We study the percolation properties of this region for which we place a Poisson point process of intensity $\lambda$ on the region $L$. At each point of the process we centre a box of a random side length $\rho$. In case $ \rho \leq R$ for some fixed $R > 0$ we study the critical intensity $\lambda_c$ of percolation.

[This is a joint work with Rahul Roy and Anish Sarkar]