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2019 A note on the Pennington-Worah distribution
S. Péché
Electron. Commun. Probab. 24: 1-7 (2019). DOI: 10.1214/19-ECP262

Abstract

This paper is concerned with a new expression of the so-called Pennington-Worah distribution, characterizing the asymptotic empirical eigenvalue distribution of some non linear random matrix ensembles. More precisely consider $M= \frac{1} {m} YY^{*}$ with $Y=f(WX)$ where $W$ and $X$ are random rectangular matrices with i.i.d. centered entries. The function $f$ is applied pointwise and can be seen as an activation function in (random) neural networks. The asymptotic empirical distribution of this ensemble has been computed in [16] and [3]. Here it is related to the Marcenko-Pastur distribution and information plus noise matrices.

Citation

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S. Péché. "A note on the Pennington-Worah distribution." Electron. Commun. Probab. 24 1 - 7, 2019. https://doi.org/10.1214/19-ECP262

Information

Received: 21 May 2019; Accepted: 21 August 2019; Published: 2019
First available in Project Euclid: 31 October 2019

zbMATH: 1423.60032
MathSciNet: MR4029435
Digital Object Identifier: 10.1214/19-ECP262

Subjects:
Primary: 60E05

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