K. Simon

Random Survivor Sets with Moving Holes in Bedford-McMullen Carpets

Let $2\le m<n$ be integers, and let $K(\mathcal{A})$ be the Bedford--McMullen carpet generated by $\{(x,y)\mapsto((x+i)/m,(y+j)/n):(i,j)\in\mathcal{A}\}$, where $\mathcal{A}$ is a subset of $\{0,1,\ldots,m-1\}\times\{0,1,\ldots,n-1\}$. Write $\mathcal{B}$ for the set of occupied columns, and assume that $\#\mathcal{B}\...