# Sharp bounds for sums associated to graphs of matrices

```@article{Mingo2012SharpBF,
title={Sharp bounds for sums associated to graphs of matrices},
author={J. Mingo and R. Speicher},
journal={Journal of Functional Analysis},
year={2012},
volume={262},
pages={2272-2288}
}```
• Published 2012
• Mathematics
• Journal of Functional Analysis
• We provide a simple algorithm for finding the optimal upper bound for sums of products of matrix entries of the form Sπ(N):=∑j1,…,j2m=1kerj⩾πNtj1j2(1)tj3j4(2)⋯tj2m−1j2m(m) where some of the summation indices are constrained to be equal. The upper bound is easily obtained from a graph Gπ associated to the constraints, π, in the sum.

#### References

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Free Probability and Random Matrices, to appear in the Fields Institute Monograph Series