Completing the picture for the smallest eigenvalue of real Wishart matrices

Akemann G, Guhr T, Kieburg M, Wegner R, Wirtz T (2014)
Physical Review Letters 113(5): 250201.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Akemann, GernotUniBi; Guhr, T.; Kieburg, MarioUniBi; Wegner, R.; Wirtz, T.
Abstract / Bemerkung
Rectangular real $N \times (N + \nu)$ matrices $W$ with a Gaussiandistribution appear very frequently in data analysis, condensed matter physicsand quantum field theory. A central question concerns the correlations encodedin the spectral statistics of $WW^T$. The extreme eigenvalues of $W W^T$ are ofparticular interest. We explicitly compute the distribution and the gapprobability of the smallest non-zero eigenvalue in this ensemble, both forarbitrary fixed $N$ and $\nu$, and in the universal large $N$ limit with $\nu$fixed. We uncover an integrable Pfaffian structure valid for all even values of$\nu\geq 0$. This extends previous results for odd $\nu$ at infinite $N$ andrecursive results for finite $N$ and for all $\nu$. Our mathematical resultsinclude the computation of expectation values of half integer powers ofcharacteristic polynomials.
Erscheinungsjahr
2014
Zeitschriftentitel
Physical Review Letters
Band
113
Ausgabe
5
Art.-Nr.
250201
ISSN
0031-9007
eISSN
1079-7114
Page URI
https://pub.uni-bielefeld.de/record/2696621

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Akemann G, Guhr T, Kieburg M, Wegner R, Wirtz T. Completing the picture for the smallest eigenvalue of real Wishart matrices. Physical Review Letters. 2014;113(5): 250201.
Akemann, G., Guhr, T., Kieburg, M., Wegner, R., & Wirtz, T. (2014). Completing the picture for the smallest eigenvalue of real Wishart matrices. Physical Review Letters, 113(5), 250201. doi:10.1103/PhysRevLett.113.250201
Akemann, G., Guhr, T., Kieburg, M., Wegner, R., and Wirtz, T. (2014). Completing the picture for the smallest eigenvalue of real Wishart matrices. Physical Review Letters 113:250201.
Akemann, G., et al., 2014. Completing the picture for the smallest eigenvalue of real Wishart matrices. Physical Review Letters, 113(5): 250201.
G. Akemann, et al., “Completing the picture for the smallest eigenvalue of real Wishart matrices”, Physical Review Letters, vol. 113, 2014, : 250201.
Akemann, G., Guhr, T., Kieburg, M., Wegner, R., Wirtz, T.: Completing the picture for the smallest eigenvalue of real Wishart matrices. Physical Review Letters. 113, : 250201 (2014).
Akemann, Gernot, Guhr, T., Kieburg, Mario, Wegner, R., and Wirtz, T. “Completing the picture for the smallest eigenvalue of real Wishart matrices”. Physical Review Letters 113.5 (2014): 250201.

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PMID: 25554862
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arXiv: 1409.0360

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