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- W4290802279 abstract "Let $$ X_{n} $$ be $$ ntimes N $$ random complex matrices, and let $$R_{n}$$ and $$T_{n}$$ be non-random complex matrices with dimensions $$ntimes N$$ and $$ntimes n$$ , respectively. We assume that the entries of $$ X_{n} $$ are normalized independent random variables satisfying the Lindeberg condition, $$ T_{n} $$ are nonnegative definite Hermitian matrices and commutative with $$R_nR_n^*$$ , i.e., $$T_{n}R_{n}R_{n}^{*}= R_{n}R_{n}^{*}T_{n} $$ . The general information-plus-noise-type matrices are defined by $$C_{n}=frac{1}{N}T_{n}^{frac{1}{2}} left( R_{n} +X_{n}right) left( R_{n}+X_{n}right) ^{*}T_{n}^{frac{1}{2}} $$ . In this paper, we establish the limiting spectral distribution of the large-dimensional general information-plus-noise-type matrices $$C_{n}$$ . Specifically, we show that as n and N tend to infinity proportionally, the empirical distribution of the eigenvalues of $$C_{n}$$ converges weakly to a non-random probability distribution, which is characterized in terms of a system of equations of its Stieltjes transform." @default.
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- W4290802279 date "2022-08-11" @default.
- W4290802279 modified "2023-10-09" @default.
- W4290802279 title "The Limiting Spectral Distribution of Large-Dimensional General Information-Plus-Noise-Type Matrices" @default.
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- W4290802279 doi "https://doi.org/10.1007/s10959-022-01193-x" @default.
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