Discrete Isoperimetric Inequalities via Curvature

Classical isoperimetric inequalities on the Boolean hypercube can extend beyond independent product measures. The talk proves KKL, Talagrand and Eldan–Gross inequalities under a Dobrushin-type weak-dependence condition, including a class of Ising models. The method combines semigroup arguments, discrete Bakry–Émery theory and gradient estimates.