We consider independent long-range percolation on the integer lattice where the vertices are connected with probability proportional to some negative power of their Euclidean distance. We study different percolation critical exponents. Using a connection between the critical exponents and the isoperimetry of cubes in the integer lattice, we show sharp lower bounds on these exponents in dimension 1 and for suitable domains of the polynomial decay.
Based on joint work with Noam Berger (https://arxiv.org/abs/2204.12410).