# Diffusion processes and the asymptotic bulk gap probability for the real Ginibre ensemble

@article{Forrester2013DiffusionPA, title={Diffusion processes and the asymptotic bulk gap probability for the real Ginibre ensemble}, author={Peter J. Forrester}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2013}, volume={48} }

It is known that the bulk scaling limit of the real eigenvalues for the real Ginibre ensemble is equal in distribution to the rescaled t → ∞ ?> limit of the annihilation process A + A → ∅ ?> . Furthermore, deleting each particle at random in the rescaled t → ∞ ?> limit of the coalescence process A + A → A ?> , a process equal in distribution to the annihilation process results. We use these inter-relationships to deduce from the existing literature the asymptotic small and large distance form…

## 17 Citations

Edge Distribution of Thinned Real Eigenvalues in the Real Ginibre Ensemble

- MathematicsAnnales Henri Poincaré
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This paper is concerned with the explicit computation of the limiting distribution function of the largest real eigenvalue in the real Ginibre ensemble when each real eigenvalue has been removed…

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Motivated by the phenomenon of duality for interacting particle systems we introduce two classes of Pfaffian kernels describing a number of Pfaffian point processes in the ‘bulk’ and at the ‘edge’.…

PR ] 1 S ep 2 02 1 Fluctuations and correlations for products of real asymmetric random matrices Will FitzGerald

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We study the real eigenvalue statistics of products of independent real Ginibre random matrices. These are matrices all of whose entries are real i.i.d. standard Gaussian random variables. For such…

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- Mathematics
- 2019

Let λmax be a shifted maximal real eigenvalue of a random N×N matrix with independent N(0, 1) entries (the ‘real Ginibre matrix’) in the N → ∞ limit. It was shown by Poplavskyi, Tribe, Zaboronski [9]…

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We consider the ensemble of real Ginibre matrices conditioned to have positive fraction $$\alpha >0$$α>0 of real eigenvalues. We demonstrate a large deviations principle for the joint eigenvalue…

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- Mathematics
- 2016

Let $\sqrt{N}+\lambda_{max}$ be the largest real eigenvalue of a random $N\times N$ matrix with independent $N(0,1)$ entries (the `real Ginibre matrix'). We study the large deviations behaviour of…

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- Mathematics, Computer ScienceExp. Math.
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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.

The largest real eigenvalue in the real Ginibre ensemble and its relation to the Zakharov–Shabat system

- Mathematics
- 2018

The real Ginibre ensemble consists of $n\times n$ real matrices ${\bf X}$ whose entries are i.i.d. standard normal random variables. In sharp contrast to the complex and quaternion Ginibre ensemble,…

The Probability That All Eigenvalues are Real for Products of Truncated Real Orthogonal Random Matrices

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The probability that all eigenvalues of a product of m independent $$N \times N$$N×N subblocks of a Haar distributed random real orthogonal matrix of size $$(L_i+N) \times (L_i+N)$$(Li+N)×(Li+N),…

On the solution of the Zakharov-Shabat system, which arises in the analysis of the largest real eigenvalue in the real Ginibre ensemble

- Mathematics
- 2019

Let $\lambda_{max}$ be a shifted maximal real eigenvalue of a random $N\times N$ matrix with independent $N(0,1)$ entries (the `real Ginibre matrix') in the $N\to\infty$ limit. It was shown by…

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