4 papers
Tree convolution for probability distributions with unbounded support
Ethan Davis, David Jekel, Zhichao Wang
We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in "An operad of non-commutative independences defined by trees" (Dis…
Spectra of the Conjugate Kernel and Neural Tangent Kernel for linear-width neural networks
Zhou Fan, Zhichao Wang
We study the eigenvalue distributions of the Conjugate Kernel and Neural Tangent Kernel associated to multi-layer feedforward neural networks. In an asymptotic regime where network…
Principal components in linear mixed models with general bulk
Zhou Fan, Yi Sun, Zhichao Wang
We study the principal components of covariance estimators in multivariate mixed-effects linear models. We show that, in high dimensions, the principal eigenvalues and eigenvectors…
Central Limit Theorems for a Stationary Semicircular Sequence in Free Probability
Zhichao Wang
In this paper, we focus on studying central limit theorems for functionals of some specific stationary random processes. In classical probability theory, it is well-known that for…