Some Remarks on Random Vectors and O(n)-Invariants

03/01/2023

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by   Alexander Kushkuley, et al.

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Computations involving invariant random vectors are directly related to the theory of invariants (cf. e.g <cit.>). Some simple observations along these lines are presented in this paper. We note in particular that sum of elements of the standard basis of O(n)-invariants is equal to the expectation of a random Veronese tensor up to a known scalar multiplier.