Maximum moments of sum of independent random matrices
March Boedihardjo
TL;DR
This paper establishes that the maximum moments of sums of independent positive semidefinite random matrices are achieved under specific structured conditions involving scalar multiplications of the identity matrix.
Contribution
It characterizes the extremal configurations for the moments of sums of independent positive semidefinite matrices with bounded norms.
Findings
Maximum moments are attained when matrices are scalar multiples of the identity.
The result applies to matrices with given norm bounds and expectation norms.
Provides a characterization of extremal random matrix configurations.
Abstract
We show that the maximum moments of the sum of independent positive semidefinite random matrices with given norm upper bounds and norms of expectations is attained when all the random matrices are the multiplications of certain random variables and the identity matrix.
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Taxonomy
TopicsRandom Matrices and Applications · Point processes and geometric inequalities · Probability and Risk Models