3 Hits in 6.2 sec

Overlaps, Eigenvalue Gaps, and Pseudospectrum under real Ginibre and Absolutely Continuous Perturbations [article]

Jess Banks and Jorge Garza Vargas and Archit Kulkarni and Nikhil Srivastava
2020 arXiv   pre-print
In fact, we show the above statements hold in the more general setting of non-Gaussian perturbations with real, independent, absolutely continuous entries with a finite moment assumption and appropriate  ...  This yields sharp control on the area of the pseudospectrum Λ_ϵ(A+γ G_n) in terms of the pseudospectral parameter ϵ>0, which is sufficient to bound the overlaps and eigenvector condition number via a limiting  ...  Acknowledgments We thank Amol Aggarwal, Nick Cook, Hoi Nguyen, and Stanisław Szarek for helpful conversations.  ... 
arXiv:2005.08930v1 fatcat:ocuftxwhnfc3xlar3gepgndi7e

Randomly coupled differential equations with elliptic correlations [article]

László Erdős, Torben Krüger, David Renfrew
2021 arXiv   pre-print
We rigorously prove and slightly correct the explicit formula from [28] on the time decay as a function of the asymmetry parameter.  ...  Our main tool is an asymptotically precise formula for the normalized trace of f(X) g(X^*), in the large N limit, where f and g are analytic functions.  ...  DR would like to thank Nicolas Brunel and Johnatan Aljadeff for fruitful discussions as well sharing unpublished notes.  ... 
arXiv:1908.05178v3 fatcat:x7fdeuzesbgmljotacpl5elsdq

Non-Hermitian Physics [article]

Yuto Ashida, Zongping Gong, Masahito Ueda
2020 arXiv   pre-print
/subjects in quantum regimes, such as quantum resonances, superradiance, continuous quantum Zeno effect, quantum critical phenomena, Dirac spectra in quantum chromodynamics, and nonunitary conformal field  ...  A review is given on the foundations and applications of non-Hermitian classical and quantum physics.  ...  Moreover,Ṽ contains V ∪ W and may have a nonzero overlap with W\V. different eigenvalue λ .  ... 
arXiv:2006.01837v1 fatcat:ol3sszpdvneejg7mgywm7abj64