Generalization of the Marčenko-Pastur problem
We study the spectrum of generalized Wishart matrices, defined as F=(XY^{⊤}+YX^{⊤})/2T, where X and Y are N×T matrices with zero mean, unit variance independent and identically distributed entries and such that E[X_{it}Y_{jt}]=cδ_{i,j}. The limit c=1 corresponds to the Marčenko-Pastur problem. For a...
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| Published in: | Physical review. E Vol. 102; no. 6-1; p. 062117 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
01.12.2020
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| ISSN: | 2470-0053, 2470-0053 |
| Online Access: | Get more information |
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| Summary: | We study the spectrum of generalized Wishart matrices, defined as F=(XY^{⊤}+YX^{⊤})/2T, where X and Y are N×T matrices with zero mean, unit variance independent and identically distributed entries and such that E[X_{it}Y_{jt}]=cδ_{i,j}. The limit c=1 corresponds to the Marčenko-Pastur problem. For a general c, we show that the Stieltjes transform of F is the solution of a cubic equation. In the limit c=0, T≫N, the density of eigenvalues converges to the Wigner semicircle. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 2470-0053 2470-0053 |
| DOI: | 10.1103/PhysRevE.102.062117 |