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@article{Nemirovski2007SumsOR, title={Sums of random symmetric matrices and quadratic optimization under orthogonality constraints}, author={Arkadi Nemirovski}, journal={Math. Program.}, year={2007}, volume={109}, pages={283-317} }

- Published 2007 in Math. Program.
DOI:10.1007/s10107-006-0033-0

Let Bi be deterministic real symmetric m × m matrices, and ξi be independent random scalars with zero mean and “of order of one” (e.g., ξi ∼ N (0, 1)). We are interested to know under what conditions “typical norm” of the random matrix SN = ∑Ni=1 ξiBi is of order of 1. An evident necessary condition is E{SN} O(1)I, which, essentially, translates to ∑N i=1 Bi I; a natural conjecture is that the latter condition is sufficient as well. In the paper, we prove a relaxed version of this conjecture… CONTINUE READING

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