# Extremal singular values of random matrix products and Brownian motion on GL(N,C)

@inproceedings{Ahn2022ExtremalSV, title={Extremal singular values of random matrix products and Brownian motion on GL(N,C)}, author={Andrew Ahn}, year={2022} }

We establish universality for the largest singular values of products of random matrices with right unitarily invariant distributions, in a regime where the number of matrix factors and size of the matrices tend to infinity simultaneously. The behavior of the largest log singular values coincides with the large N limit of Dyson Brownian motion with a characteristic drift vector consisting of equally spaced coordinates, which matches the large N limit of the largest log singular values of…

## Figures from this paper

## One Citation

### Lyapunov exponents for truncated unitary and Ginibre matrices

- Mathematics
- 2021

In this note, we show that the Lyapunov exponents of mixed products of random truncated Haar unitary and complex Ginibre matrices are asymptotically given by equally spaced ‘picket-fence’ statistics.…

## References

SHOWING 1-10 OF 78 REFERENCES

### Limits and fluctuations of p-adic random matrix products

- MathematicsSelecta Mathematica
- 2021

We show that singular numbers (also known as invariant factors or Smith normal forms) of products and corners of random matrices over $\mathbb{Q}_p$ are governed by the Hall-Littlewood polynomials,…

### Gaussian fluctuations for products of random matrices

- MathematicsAmerican Journal of Mathematics
- 2022

abstract:We study global fluctuations for singular values of $M$-fold products of several right-unitarily invariant $N\times N$ random matrix ensembles. As $N\to\infty$, we show the fluctuations of…

### Product Matrix Processes as Limits of Random Plane Partitions

- MathematicsInternational Mathematics Research Notices
- 2019

We consider a random process with discrete time formed by squared singular values of products of truncations of Haar-distributed unitary matrices. We show that this process can be understood as a…

### The distribution of Lyapunov exponents: Exact results for random matrices

- Mathematics
- 1986

Simple exact expressions are derived for all the Lyapunov exponents of certainN-dimensional stochastic linear dynamical systems. In the case of the product of independent random matrices, each of…

### Singular Value Statistics of Matrix Products with Truncated Unitary Matrices

- Mathematics
- 2015

We prove that the squared singular values of a fixed matrix multiplied with a truncation of a Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is applied to a…

### Universality of local spectral statistics of products of random matrices.

- MathematicsPhysical review. E
- 2020

The local spectral statistics of the considered random matrix products is identical with the local statistics of Dyson Brownian motion with the initial condition given by equidistant positions, with the crucial difference that this equivalence holds only locally.

### 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…

### Lyapunov exponents for truncated unitary and Ginibre matrices

- Mathematics
- 2021

In this note, we show that the Lyapunov exponents of mixed products of random truncated Haar unitary and complex Ginibre matrices are asymptotically given by equally spaced ‘picket-fence’ statistics.…

### Determinantal Processes with Number Variance Saturation

- Mathematics
- 2004

Consider Dyson’s Hermitian Brownian motion model after a finite time S, where the process is started at N equidistant points on the real line. These N points after time S form a determinantal process…

### Crystallization of random matrix orbits

- Mathematics
- 2017

Three operations on eigenvalues of real/complex/quaternion (corresponding to $\beta=1,2,4$) matrices, obtained from cutting out principal corners, adding, and multiplying matrices can be extrapolated…