Distribution of Singular Values of Random Band Matrices; Marchenko–Pastur Law and More
نویسندگان
چکیده
منابع مشابه
More about measures and Jacobians of singular random matrices
In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
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in this work are studied the jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.
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Let ξ be a real-valued random variable of mean zero and variance 1. Let Mn(ξ) denote the n × n random matrix whose entries are iid copies of ξ and σn(Mn(ξ)) denote the least singular value of Mn(ξ). The quantity σn(Mn(ξ)) 2 is thus the least eigenvalue of the Wishart matrix MnM ∗ n. We show that (under a finite moment assumption) the probability distribution nσn(Mn(ξ)) 2 is universal in the sen...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2017
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-017-1844-5