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math.PR2019★ 3 cited
Universality of the least singular value for the sum of random matrices
Ziliang Che, Patrick Lopatto
We consider the least singular value of , where are independent Haar-distributed unitary matrices and are deterministic diagonal matrices. Un…
math.PR2019
Tail bounds for gaps between eigenvalues of sparse random matrices
Patrick Lopatto, Kyle Luh
We prove the first eigenvalue repulsion bound for sparse random matrices. As a consequence, we show that these matrices have simple spectrum, improving the range of sparsity and er…