# Convergence rate for spectral distribution of addition of random matrices

Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 319, 251–291.

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Abstract

Let A and B be two N by N deterministic Hermitian matrices and let U be an N by N Haar distributed unitary matrix. It is well known that the spectral distribution of the sum H = A + UBU∗ converges weakly to the free additive convolution of the spectral distributions of A and B, as N tends to infinity. We establish the optimal convergence rate in the bulk of the spectrum.

Publishing Year

Date Published

2017-10-15

Journal Title

Advances in Mathematics

Acknowledgement

Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation

Volume

319

Page

251 - 291

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### Cite this

Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition of random matrices.

*Advances in Mathematics*. 2017;319:251-291. doi:10.1016/j.aim.2017.08.028Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices.

*Advances in Mathematics*. Academic Press. https://doi.org/10.1016/j.aim.2017.08.028Bao, Zhigang, László Erdös, and Kevin Schnelli. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.”

*Advances in Mathematics*. Academic Press, 2017. https://doi.org/10.1016/j.aim.2017.08.028.Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,”

*Advances in Mathematics*, vol. 319. Academic Press, pp. 251–291, 2017.Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.”

*Advances in Mathematics*, vol. 319, Academic Press, 2017, pp. 251–91, doi:10.1016/j.aim.2017.08.028.**All files available under the following license(s):**

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