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| 2. |
- Bao, Zhigang, et al.
(författare)
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Equipartition principle for Wigner matrices
- 2021
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Ingår i: Forum of Mathematics, Sigma. - : Cambridge University Press (CUP). - 2050-5094. ; 9
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices.
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| 3. |
- Bao, Zhigang, et al.
(författare)
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LOCAL SINGLE RING THEOREM ON OPTIMAL SCALE
- 2019
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Ingår i: Annals of Probability. - : Institute of Mathematical Statistics. - 0091-1798 .- 2168-894X. ; 47:3, s. 1270-1334
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Tidskriftsartikel (refereegranskat)abstract
- Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Sigma be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189-1217] asserts that the empirical eigenvalue distribution of the matrix X : = U Sigma V* converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in C. Within the bulk regime, that is, in the interior of the single ring, we establish the convergence of the empirical eigenvalue distribution on the optimal local scale of order N-1/2+epsilon and establish the optimal convergence rate. The same results hold true when U and V are Haar distributed on O(N).
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| 4. |
- Bao, Zhigang, et al.
(författare)
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On the support of the free additive convolution
- 2020
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Ingår i: Journal d'Analyse Mathematique. - : Springer Nature. - 0021-7670 .- 1565-8538. ; 142:1, s. 323-348
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Tidskriftsartikel (refereegranskat)abstract
- We consider the free additive convolution of two probability measures mu and nu on the real line and show that mu boxed plus nu is supported on a single interval if mu and nu each has single interval support. Moreover, the density of mu boxed plus nu is proven to vanish as a square root near the edges of its support if both mu and nu have power law behavior with exponents between -1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5].
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| 5. |
- Quaglia, Federica, et al.
(författare)
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DisProt in 2022 : improved quality and accessibility of protein intrinsic disorder annotation
- 2022
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Ingår i: Nucleic Acids Research. - : Oxford University Press (OUP). - 0305-1048 .- 1362-4962. ; 50:D1, s. D480-D487
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Tidskriftsartikel (refereegranskat)abstract
- The Database of Intrinsically Disordered Proteins (DisProt, URL: https://disprot.org) is the major repository of manually curated annotations of intrinsically disordered proteins and regions from the literature. We report here recent updates of DisProt version 9, including a restyled web interface, refactored Intrinsically Disordered Proteins Ontology (IDPO), improvements in the curation process and significant content growth of around 30%. Higher quality and consistency of annotations is provided by a newly implemented reviewing process and training of curators. The increased curation capacity is fostered by the integration of DisProt with APICURON, a dedicated resource for the proper attribution and recognition of biocuration efforts. Better interoperability is provided through the adoption of the Minimum Information About Disorder (MIADE) standard, an active collaboration with the Gene Ontology (GO) and Evidence and Conclusion Ontology (ECO) consortia and the support of the ELIXIR infrastructure.
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