Short Talk: Panagiotis Spanos

We study the model of spread-out percolation, originally introduced in \mathbb{Z}^d by Hara and Slade. This model depends on a distance parameter, but the percolated graph retains the same expected degree at each vertex as the parameter grows. We present a natural generalization to all vertex-transitive graphs. In the case of transitive graphs with superlinear polynomial growth, we prove that the critical value for the expected degree of each vertex converges to 1 as the distance parameter tends to infinity. This extends a well-known result in  \mathbb{Z}^d for $d≥2$, established by Penrose. Based on joint work with Matthew Tointon.