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This book gives an overview of works concerning large deviations and moment problems. The topics covered include the use of large deviations to build barrier functions for general moment spaces, asymptotic properties of distributions on moment spaces and applications to matrix moment problems, randomized moment problems and random matrices, and finally recent results on sum rules using the large deviation properties of random spectral measures.

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Fabrice Gamboa, U. Paul Sabatier, France; Jan Nagel, TU Eindhoven, The Netherlands; Alain Rouault, U. Paris-Saclay, France.

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