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We characterize the growth of the Sibson and Arimoto mutual informations and$\alpha$-maximal leakage, of any order that is at least unity, between a randomvariable and a growing set of noisy, conditionally independent andidentically-distributed observations of the random variable. Each of thesemeasures increases exponentially fast to a limit that is order- andmeasure-dependent, with an exponent that is order- and measure-independent.

Strong Asymptotic Composition Theorems for Mutual Information Measures