Establishes W1 quantitative bounds for Laplace-type convergence of measures with norm-like potentials using coarea formula under generalized Jacobian invertibility, applied to maxent and SGLD.
Approximation of integrals over asymptotic sets with applications to probability and statistics
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abstract
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate tails of quadratic forms of random vectors, supremum of random linear forms among others. Applications to the study of finite size random matrices, finite sample statistics of autoregressive processes, and supremum of some stochastic processes.
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2021 1verdicts
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On quantitative Laplace-type convergence results for some exponential probability measures, with two applications
Establishes W1 quantitative bounds for Laplace-type convergence of measures with norm-like potentials using coarea formula under generalized Jacobian invertibility, applied to maxent and SGLD.