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Explore second-order Poincaré inequalities and related convergence results in this 50-minute lecture on stochastic geometry. Delve into a new collection of probabilistic bounds on the Poisson space, measuring the distance to Gaussianity for random elements with 'two-scale stabilization'. Examine how these estimates, inspired by Chatterjee and Sen's work on quantitative CLT for minimal spanning tree length, are tailored for weakly stabilizing functionals. Discover novel quantitative bounds applicable to strongly stabilizing functionals with minimal assumptions on stabilization radii. Learn about the joint work of Peccati, Lachièze-Rey, and Yang in advancing variational techniques in stochastic geometry.
