Erratum: Some patterned matrices with independent entries (Random Matrices: Theory Appl (2021) 10:3 (2150030) DOI: 10.1142/S2010326321500301)

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Research Article

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Random Matrices: Theory and Application


Lemma 6.2 is incorrect. Hence the proof of condition (ii) of Lemma 6.1 is invalid and so the almost sure (a.s.) convergence claim of the ESDs in Theorems 3.1 3.3 are in general invalid, though the convergence of the EESDs remain valid. For certain special cases, a.s. convergence remain valid. The proofs of the facts that the entries can be assumed to have mean zero and bounded by tn change. The a.s. convergence of the ESDs for matrices with general triangular i.i.d. entries in Sec. 7.2.1 and for matrices with a variance profile in Sec. 7.3 are now invalid. However, the convergence of the EESDs hold.We refer to any equations (a.b) from [2] as (a.b-o) here. Corrections in the statements of Theorems 3.1–3.3: In Theorem 3.1, the following changes are required: (i) The statement in part (a) should be replaced by “the EESD of Zn converges weakly to a symmetric probability measure µ, say.” (ii) In part (b), (3.3-o) should be now replaced by (Equtions Presented).



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