# Real spectra of large real asymmetric random matrices.

@article{Tarnowski2021RealSO, title={Real spectra of large real asymmetric random matrices.}, author={Wojciech Tarnowski}, journal={Physical review. E}, year={2021}, volume={105 1}, pages={ L012104 } }

When a randomness is introduced at the level of real matrix elements, depending on its particular realization, a pair of eigenvalues can appear as real or form a complex conjugate pair. We show that in the limit of large matrix size the density of such real eigenvalues is proportional to the square root of the asymptotic density of complex eigenvalues continuated to the real line. This relation allows one to calculate the real densities up to a normalization constant, which is then applied to…

## One Citation

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## References

SHOWING 1-10 OF 49 REFERENCES

### Eigenvalue statistics of random real matrices.

- Computer Science, MathematicsPhysical review letters
- 1991

The joint probability density of eigenvalues in a Gaussian ensemble of real asymmetric matrices, which is invariant under orthogonal transformations is determined, which indicates thatrices of the type considered appear in models for neural-network dynamics and dissipative quantum dynamics.

### Truncations of random orthogonal matrices.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

An exact formula for the density of eigenvalues is derived which consists of two components: finite fraction ofeigenvalues are real, while the remaining part of the spectrum is located inside the unit disk symmetrically with respect to the real axis.

### How Many Eigenvalues of a Product of Truncated Orthogonal Matrices are Real?

- Mathematics, Computer ScienceExp. Math.
- 2020

This paper exploits the fact that the eigenvalues of Pm form a Pfaffian point process to obtain an explicit determinant expression for the probability of finding any given number of real eigen values.

### Spectra of sparse non-hermitian random matrices: an analytical solution.

- Computer SciencePhysical review letters
- 2012

It is shown analytically that the convergence rate of a transport process on a very sparse graph depends in a nonmonotonic way upon the degree of symmetry of the graph edges.

### The Ginibre Ensemble of Real Random Matrices and its Scaling Limits

- Computer Science
- 2009

We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a 2 × 2 matrix kernel…

### Statistical Ensembles of Complex, Quaternion, and Real Matrices

- Mathematics
- 1965

Statistical ensembles of complex, quaternion, and real matrices with Gaussian probability distribution, are studied. We determine the over‐all eigenvalue distribution in these three cases (in the…

### Spectral theory of sparse non-Hermitian random matrices

- Mathematics, Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2019

It is shown how the spectra of sparse non-Hermitian matrices can be computed via an analogy with infinite dimensional operators obeying certain recursion relations, and the use of these methods to obtain both analytic and numerical results for the spectrum.

### Eigenvalue statistics of the real Ginibre ensemble.

- MathematicsPhysical review letters
- 2007

A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented, relevant to May's stability analysis of biological webs.

### On the number of real eigenvalues of a product of truncated orthogonal random matrices

- MathematicsElectronic Journal of Probability
- 2022

Let O be chosen uniformly at random from the group of ( N + L ) × ( N + L ) orthogonal matrices. Denote by ˜ O the upper-left N × N corner of O , which we refer to as a truncation of O . In this…

### How many eigenvalues of a random matrix are real

- Mathematics
- 1994

Let A be an n x n matrix whose elements are independent random variables with standard normal distributions. As n oo , the expected number of real eigenvalues is asymptotic to V/7r . We obtain a…