Matrix anti-concentration inequalities with applications
Z Nie - Proceedings of the 54th Annual ACM SIGACT …, 2022 - dl.acm.org
We study m by m random matrices M with jointly Gaussian entries. Assuming a global small-
ball probability bound inf x, y∈ S m− 1 ℙ⎛⎝⎪⎪ x* M y⎪⎪> m− O (1)⎞⎠≥ 1/2 and a …
ball probability bound inf x, y∈ S m− 1 ℙ⎛⎝⎪⎪ x* M y⎪⎪> m− O (1)⎞⎠≥ 1/2 and a …
The singularity probability of a random symmetric matrix is exponentially small
M Campos, M Jenssen, M Michelen… - Journal of the American …, 2024 - ams.org
The singularity probability of a random symmetric matrix is exponentially small Page 1
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY https://doi.org/10.1090/jams/1042 …
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY https://doi.org/10.1090/jams/1042 …
Singularity of discrete random matrices
Let ξ ξ be a non-constant real-valued random variable with finite support and let M_ n (ξ) M n
(ξ) denote an n * nn× n random matrix with entries that are independent copies of ξ ξ. For ξ ξ …
(ξ) denote an n * nn× n random matrix with entries that are independent copies of ξ ξ. For ξ ξ …
Random matrix theory and its applications
AJ Izenman - Statistical Science, 2021 - projecteuclid.org
This article reviews the important ideas behind random matrix theory (RMT), which has
become a major tool in a variety of disciplines, including mathematical physics, number …
become a major tool in a variety of disciplines, including mathematical physics, number …
Extreme singular values of inhomogeneous sparse random rectangular matrices
I Dumitriu, Y Zhu - arXiv preprint arXiv:2209.12271, 2022 - arxiv.org
We develop a unified approach to bounding the largest and smallest singular values of an
inhomogeneous random rectangular matrix, based on the non-backtracking operator and …
inhomogeneous random rectangular matrix, based on the non-backtracking operator and …
Singularity of sparse Bernoulli matrices
AE Litvak, KE Tikhomirov - Duke Mathematical Journal, 2022 - projecteuclid.org
Let M n be an n× n random matrix with independent and identically distributed Bernoulli (p)
entries. We show that there is a universal constant C≥ 1 such that, whenever p and n satisfy …
entries. We show that there is a universal constant C≥ 1 such that, whenever p and n satisfy …
Asymptotic geometric analysis: achievements and perspective
V Milman - Geometric Aspects of Functional Analysis: Israel …, 2023 - Springer
The reader will have noticed the non-standard appearance of this piece. Indeed, we are
used to reading papers which are either survey papers or research ones (or a mixture of …
used to reading papers which are either survey papers or research ones (or a mixture of …
Optimal minimax rate of learning interaction kernels
X Wang, I Seroussi, F Lu - arXiv preprint arXiv:2311.16852, 2023 - arxiv.org
Nonparametric estimation of nonlocal interaction kernels is crucial in various applications
involving interacting particle systems. The inference challenge, situated at the nexus of …
involving interacting particle systems. The inference challenge, situated at the nexus of …
Quantitative invertibility of non-Hermitian random matrices
K Tikhomirov - arXiv preprint arXiv:2206.00601, 2022 - arxiv.org
The problem of estimating the smallest singular value of random square matrices is
important in connection with matrix computations and analysis of the spectral distribution. In …
important in connection with matrix computations and analysis of the spectral distribution. In …
The least singular value of a random symmetric matrix
M Campos, M Jenssen, M Michelen… - Forum of Mathematics …, 2024 - cambridge.org
The least singular value of a random symmetric matrix Page 1 Forum of Mathematics, Pi (2024),
Vol. 12:e3 1–69 doi:10.1017/fmp.2023.29 RESEARCH ARTICLE The least singular value of a …
Vol. 12:e3 1–69 doi:10.1017/fmp.2023.29 RESEARCH ARTICLE The least singular value of a …