# Random matrix-valued multiplicative functions and linear recurrences in Hilbert-Schmidt norms of random matrices

@article{Gerspach2018RandomMM, title={Random matrix-valued multiplicative functions and linear recurrences in Hilbert-Schmidt norms of random matrices}, author={Maxim Gerspach}, journal={arXiv: Number Theory}, year={2018} }

We introduce the notion of a random matrix-valued multiplicative function, generalizing Rademacher random multiplicative functions to matrices. We provide an asymptotic for the second moment based on a linear recurrence property for Hilbert-Schmidt norms of sucessive products of random matrices. Moreover, we provide upper bounds for the higher even moments related to the generalized joint spectral radius.

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