A limit theorem at the edge of a non-Hermitian random matrix ensemble

By Brian Rider. 2003

110 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a5b30a11febf21b0a2454574465e50d931c56bb8

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Spectral Radii of Large Non-Hermitian Random Matrices (2014, background): “From [45] or (a) of Theorem 3, we know max1≤ j≤n |λ j (Xi)|/√n → 1 in probability for each i .”
Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation (2019, background): “By Rider (2003), the maximum eigenvalue of W scales like 1 +O(n−1/2) if Wij ∼ N (0, 1/n), and so does that of WL for fixed L.”
Extreme value statistics of correlated random variables: A pedagogical review (2019, background): “In these two-dimensional situations a natural extreme observable is the largest radius rmax = max1≤i≤N |zi| [224–226] (see also the discussion at the end of Section IV B 8 below).”
Random matrices: Universality of local spectral statistics of non-Hermitian matrices (2012, background): “It seems likely that one can also obtain extensions of many of the other results in [39] (or related papers, such as [32], [38]) on gaussian fluctuations from the circular law from the complex gaussian ensemble to other ensembles that match the complex gaussian ensemble to a sufficiently large numbe”
Circular law theorem for random Markov matrices (2008, background): “entries, and to [42] and [13] for the non central case. Another very interesting open problem is the ﬂuctuation of the global and extremal spectrum for which one can ﬁnd some partial answers in [43], [36], [42], [38]. Recall that the rows of M are i.i.d. and follow an exchangeable law ηn on the simp”
The circular law for random matrices (2007, background): “Rider proved in [21] and [20] results about the spectral radius and about linear statistics of eigenvalues of non-Hermitian matrices with Gaussian entries.”