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- Title
Norms of structured random matrices.
- Authors
Adamczak, Radosław; Prochno, Joscha; Strzelecka, Marta; Strzelecki, Michał
- Abstract
For m , n ∈ N , let X = (X ij) i ≤ m , j ≤ n be a random matrix, A = (a ij) i ≤ m , j ≤ n a real deterministic matrix, and X A = (a ij X ij) i ≤ m , j ≤ n the corresponding structured random matrix. We study the expected operator norm of X A considered as a random operator between ℓ p n and ℓ q m for 1 ≤ p , q ≤ ∞ . We prove optimal bounds up to logarithmic terms when the underlying random matrix X has i.i.d. Gaussian entries, independent mean-zero bounded entries, or independent mean-zero ψ r ( r ∈ (0 , 2 ] ) entries. In certain cases, we determine the precise order of the expected norm up to constants. Our results are expressed through a sum of operator norms of Hadamard products A ∘ A and (A ∘ A) T .
- Subjects
RANDOM matrices; RANDOM operators
- Publication
Mathematische Annalen, 2024, Vol 388, Issue 4, p3463
- ISSN
0025-5831
- Publication type
Article
- DOI
10.1007/s00208-023-02599-6