Corpus ID: 237513483

Lyapunov exponents for truncated unitary and Ginibre matrices

@inproceedings{Ahn2021LyapunovEF,
  title={Lyapunov exponents for truncated unitary and Ginibre matrices},
  author={Andrew Ahn and Roger Van Peski},
  year={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. We discuss how these statistics should originate from the connection between random matrix products and multiplicative Brownian motion on GLn(C), analogous to the connection between discrete random walks and ordinary Brownian motion. Our methods are based on contour integral formulas for products… Expand
1 Citations
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References

SHOWING 1-10 OF 22 REFERENCES
Lyapunov exponent, universality and phase transition for products of random matrices
We solve the problem on local statistics of finite Lyapunov exponents for $M$ products of $N\times N$ Gaussian random matrices as both $M$ and $N$ go to infinity, proposed by Akemann, Burda, KieburgExpand
Product Matrix Processes as Limits of Random Plane Partitions
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 aExpand
From integrable to chaotic systems: Universal local statistics of Lyapunov exponents
Systems where time evolution follows a multiplicative process are ubiquitous in physics. We study a toy model for such systems where each time step is given by multiplication with an independentExpand
Limits and fluctuations of p-adic random matrix products
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,Expand
Crystallization of random matrix orbits
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 extrapolatedExpand
Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis
We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a variety ofExpand
Products of Many Large Random Matrices and Gradients in Deep Neural Networks
We study products of random matrices in the regime where the number of terms and the size of the matrices simultaneously tend to infinity. Our main theorem is that the logarithm of the $$\ell _2$$ ℓExpand
On asymptotics of large Haar distributed unitary matrices
TLDR
It is shown that the renormalized truncated Haar unitaries converge to a Gaussian random matrix in distribution. Expand
Brownian Motion in a Weyl Chamber, Non-Colliding Particles, and Random Matrices
Abstract Let n particles move in standard Brownian motion in one dimension, with the process terminating if two particles collide. This is a specific case of Brownian motion constrained to stayExpand
Products of random matrices.
We derive analytic expressions for infinite products of random 2 x 2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicatedExpand
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