تقرير
Completing the picture for the smallest eigenvalue of real Wishart matrices
| العنوان: | Completing the picture for the smallest eigenvalue of real Wishart matrices |
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| المؤلفون: | Akemann, G., Guhr, T., Kieburg, M., Wegner, R., Wirtz, T. |
| المصدر: | Phys. Rev. Lett. 113, 250201 (2014) |
| سنة النشر: | 2014 |
| المجموعة: | Mathematics Condensed Matter High Energy Physics - Lattice Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Condensed Matter - Statistical Mechanics, High Energy Physics - Lattice |
| الوصف: | Rectangular real $N \times (N + \nu)$ matrices $W$ with a Gaussian distribution appear very frequently in data analysis, condensed matter physics and quantum field theory. A central question concerns the correlations encoded in the spectral statistics of $WW^T$. The extreme eigenvalues of $W W^T$ are of particular interest. We explicitly compute the distribution and the gap probability of the smallest non-zero eigenvalue in this ensemble, both for arbitrary 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 $N$ and recursive results for finite $N$ and for all $\nu$. Our mathematical results include the computation of expectation values of half integer powers of characteristic polynomials. Comment: 5 pages, 3 figuers; minor corrections; three typos corrected in comparison to the published version in PRL |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevLett.113.250201 |
| URL الوصول: | http://arxiv.org/abs/1409.0360 |
| رقم الأكسشن: | edsarx.1409.0360 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevLett.113.250201 |
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