Structured Random Matrices
By Ramon van Handel. 2016
54 citations recorded by the source corpus.
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact or approximate symmetries, such as matrices with i.i.d. entries, for which precise analytic results and limit theorems are available. Much less well understood are matrices that are endowed with an arbitrary structure, such as sparse Wigner matrices or matrices whose entries possess a given variance pattern. The challenge in investigating such structured random matrices is to understand how the given structure of the matrix is reflected in its spectral properties. This chapter reviews a number of recent results, methods, and open problems in this direction, with a particular emphasis on sharp spectral norm inequalities for Gaussian random matrices.
Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/ad91c6ccd0ab757f23b8b8a22fad6dfb318134f9
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In Applied Mathematics
In Mathematical Physics
In Statistics and Probability
- Ramon van Handel
- Afonso S. Bandeira
- March Boedihardjo
- Justin Salez
- Xiaolu Tan
- Marcel Nutz
- Nicholas A. Cook
- Nicole El Karoui
Citations in the corpus
- Matrix concentration inequalities and free probability (2021, background): “This disproves a conjecture, formulated in [37, 39, 4], which suggests that the parameter v(X) in our main results can be replaced by a certain smaller parameter σ∗(X) that will be defined below.”