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Item type:Publication, Access status: with files , Lower variance bounds and normal approximation of Poisson functionals in stochastic geometry(2024); Lower bounds for variances are often required for deriving central limit theorems. In this thesis, a generalised reverse Poincaré inequality is established, which provides a lower variance bound for Poisson functionals and depends on the difference operator of some fixed order. To show how this lower variance bound can be used, three different applications from stochastic geometry are explored: statistics of spatial random graphs in Euclidean and hyperbolic space, Lp surface areas of random polytopes in the Euclidean unit ball and geometric functionals of excursion sets of Poisson shot noise processes.Publicationtype: Doctoral Thesis83 149