Proof of the Weak Local Law for Wigner Matrices using Resolvent Expansions

Vlad Margarint

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arXiv · 1808.07092

Proof of the Weak Local Law for Wigner Matrices using Resolvent Expansions

Vlad Margarint

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Abstract

The aim of this paper is to provide a novel proof for the Local Semicircle Law for the Wigner ensemble. The core of the proof is the intensive use of the algebraic structure that arises, i.e. resolvent expansions and resolvent identities. On the analytic side, concentration of measure results and high probability bounds are used. The conclusion is obtained using a bootstrapping argument that provides information about the change of the bounds from large to small scales. This approach leads to a new and shorter proof of the Weak Local Law for Wigner Matrices, that exploits heavily the algebraic structure appearing in the setting.

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BibTeX RIS

Vlad Margarint. 2018-08-21. Proof of the Weak Local Law for Wigner Matrices using Resolvent Expansions. https://arxiv.org/abs/1808.07092

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