The Ginibre Ensemble of Real Random Matrices and its Scaling Limits
By Alexei Borodin, Christopher D. Sinclair. 2008
161 citations recorded by the source corpus.
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 associated to the ensemble. We apply this result to the real Ginibre ensemble and compute the bulk and edge scaling limits of its correlation functions as the size of the matrices becomes large.
Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/cdceeb9dd4f74248ffb93fc76342419e191f52fd
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In Discrete Mathematics and Combinatorics
- Charles Bordenave
- Van H. Vu
- Djalil CHAFAÏ
- Terence Tao
- L. Erdős
- Nicholas A. Cook
- Hoi H. Nguyen
- Roman Vershynin
In Mathematical Physics
- Charles Bordenave
- Djalil CHAFAÏ
- Van H. Vu
- Terence Tao
- Hoi H. Nguyen
- Nicholas A. Cook
- L. Erdős
- Horng-Tzer Yau
In Statistics and Probability
- Charles Bordenave
- Djalil CHAFAÏ
- Van H. Vu
- Terence Tao
- Nicholas A. Cook
- Hoi H. Nguyen
- L. Erdős
- Horng-Tzer Yau
Citations in the corpus
- Random matrices: Universality of local spectral statistics of non-Hermitian matrices (2012, methodology): “This lemma follows fairly easily from the computations in [7]; we give the details in Appendix B.”
- Around the circular law (2011, background): “Note that the square of the smallest singular value sn(n −1/2G)2 of the Complex Ginibre Ensemble follows an exponential law [40] and this result is asymptotically universal [148]; • Gap probabilities and Voronöı cells (see [3, 62] for the Ginibre Ensemble); • Linear statistics of μX (for some result”