## 6 Citations

Normal fluctuation in quantum ergodicity for Wigner matrices

- MathematicsThe Annals of Probability
- 2022

We consider the quadratic form of a general deterministic matrix on the eigenvectors of an N×N Wignermatrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the largeN limit.…

Tail bounds for gaps between eigenvalues of sparse random matrices

- Computer Science
- 2019

The first eigenvalue repulsion bound for sparse random matrices is proved, and it is shown that these matrices have simple spectrum, improving the range of sparsity and error probability from the work of the second author and Vu.

Fluctuations in Local Quantum Unique Ergodicity for Generalized Wigner Matrices

- MathematicsCommunications in Mathematical Physics
- 2022

We study the eigenvector mass distribution for generalized Wigner matrices on a set of coordinates I, where N 6 |I| 6 N1−ε, and prove it converges to a Gaussian at every energy level, including the…

Eigenstate Thermalization Hypothesis for Wigner Matrices

- MathematicsCommunications in Mathematical Physics
- 2021

We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to…

Equipartition principle for Wigner matrices

- Physics, MathematicsForum of Mathematics, Sigma
- 2021

Abstract We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a…

## References

SHOWING 1-10 OF 61 REFERENCES

Sparse general Wigner-type matrices: Local law and eigenvector delocalization

- Computer ScienceJournal of Mathematical Physics
- 2019

A local law and eigenvector delocalization for general Wigner-type matrices are proved and the first results of such kind for the sparse case down to p=\frac{g(n)log n}{n}$ with g(n)\to\infty$.

Eigenvectors distribution and quantum unique ergodicity for deformed Wigner matrices

- Mathematics, Physics
- 2017

We analyze the distribution of eigenvectors for mesoscopic, mean-field perturbations of diagonal matrices in the bulk of the spectrum. Our results apply to a generalized $N\times N$ Rosenzweig-Porter…

Wegner estimate and level repulsion for Wigner random matrices

- Mathematics
- 2008

We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive…

Eigenvector distribution of Wigner matrices

- Mathematics
- 2011

We consider N × N Hermitian or symmetric random matrices with independent entries. The distribution of the (i, j)-th matrix element is given by a probability measure νij whose first two moments…

Local Semicircle Law and Complete Delocalization for Wigner Random Matrices

- Mathematics
- 2009

We consider N × N Hermitian random matrices with independent identical distributed entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order 1/N. Under…

Delocalization of eigenvectors of random matrices with independent entries

- Mathematics
- 2015

Author(s): Rudelson, Mark; Vershynin, Roman | Abstract: We prove that an n by n random matrix G with independent entries is completely delocalized. Suppose the entries of G have zero means, variances…

No-gaps delocalization for general random matrices

- Mathematics
- 2015

We prove that with high probability, every eigenvector of a random matrix is delocalized in the sense that any subset of its coordinates carries a non-negligible portion of its $${\ell_2}$$ℓ2 norm.…

Bulk universality for Wigner matrices

- Mathematics
- 2009

We consider N × N Hermitian Wigner random matrices H where the probability density for each matrix element is given by the density ν(x) = e−U(x). We prove that the eigenvalue statistics in the bulk…

Extreme gaps between eigenvalues of Wigner matrices

- MathematicsJournal of the European Mathematical Society
- 2021

This paper proves universality of the distribution of the smallest and largest gaps between eigenvalues of generalized Wigner matrices, under some smoothness assumption for the density of the…

Fixed Energy Universality for Generalized Wigner Matrices

- Mathematics
- 2014

We prove the Wigner‐Dyson‐Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random…