Abstract
Similarly as in number theory one may define the notion of an additive function in the set of all mappings of a finite set into itself. If a mapping is sampled uniformly at random, the function becomes a sum of dependent random variables. Estimation of its variance via the sum of variances of the summands is a non-trivial problem. We give an answer analogously to the Turán-Kubilius inequality, well known in probabilistic number theory.
Zur Erinnerung an Professor Wolfgang Schwarz
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Manstavičius, E. (2016). A Turán-Kubilius Inequality on Mappings of a Finite Set. In: Sander, J., Steuding, J., Steuding, R. (eds) From Arithmetic to Zeta-Functions. Springer, Cham. https://doi.org/10.1007/978-3-319-28203-9_19
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DOI: https://doi.org/10.1007/978-3-319-28203-9_19
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