Quantitative clts in deep neural networks
We study the distribution of a fully connected neural network with random Gaussian weights
and biases in which the hidden layer widths are proportional to a large constant $ n $. Under …
and biases in which the hidden layer widths are proportional to a large constant $ n $. Under …
Gaussian random field approximation via Stein's method with applications to wide random neural networks
We derive upper bounds on the Wasserstein distance (W 1), with respect to sup-norm,
between any continuous R d valued random field indexed by the n-sphere and the …
between any continuous R d valued random field indexed by the n-sphere and the …
A spectral representation of kernel Stein discrepancy with application to goodness-of-fit tests for measures on infinite dimensional Hilbert spaces
Kernel Stein discrepancy (KSD) is a widely used kernel-based measure of discrepancy
between probability measures. It is often employed in the scenario where a user has a …
between probability measures. It is often employed in the scenario where a user has a …
[HTML][HTML] Malliavin–Stein method: a survey of some recent developments
Initiated around the year 2007, the Malliavin–Stein approach to probabilistic approximations
combines Stein's method with infinite-dimensional integration by parts formulae based on …
combines Stein's method with infinite-dimensional integration by parts formulae based on …
Stein's method of exchangeable pairs in multivariate functional approximations
C Döbler, MJ Kasprzak - 2021 - projecteuclid.org
In this paper we develop a framework for multivariate functional approximation by a suitable
Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate …
Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate …
Asymptotics for isotropic Hilbert-valued spherical random fields
A Caponera - Bernoulli, 2024 - projecteuclid.org
In this paper, we introduce the concept of isotropic Hilbert-valued spherical random field,
thus extending the notion of isotropic spherical random field to an infinite-dimensional …
thus extending the notion of isotropic spherical random field to an infinite-dimensional …
Stein's method, Gaussian processes and Palm measures, with applications to queueing
We develop a general approach to Stein's method for approximating a random process in
the path space D ([0, T]→ R d) by a real continuous Gaussian process. We then use the …
the path space D ([0, T]→ R d) by a real continuous Gaussian process. We then use the …
A quantitative central limit theorem for the simple symmetric exclusion process
B Gess, V Konarovskyi - arXiv preprint arXiv:2408.01238, 2024 - arxiv.org
A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a
$ d $-dimensional discrete torus is proven. The argument is based on a comparison of the …
$ d $-dimensional discrete torus is proven. The argument is based on a comparison of the …
High-dimensional regimes of non-stationary Gaussian correlated Wishart matrices
S Bourguin, T Dang - Random Matrices: Theory and Applications, 2022 - World Scientific
We study the high-dimensional asymptotic regimes of correlated Wishart matrices d− 1 𝒴 𝒴
T, where 𝒴 is an× d Gaussian random matrix with correlated and non-stationary entries. We …
T, where 𝒴 is an× d Gaussian random matrix with correlated and non-stationary entries. We …
The multivariate functional de Jong CLT
C Döbler, M Kasprzak, G Peccati - Probability Theory and Related Fields, 2022 - Springer
We prove a multivariate functional version of de Jong's CLT (J Multivar Anal 34 (2): 275–
289, 1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics …
289, 1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics …