This book is an invitation to the world of free probability theory. Free probability is a quite
young mathematical theory with many avatars. It owes its existence to the visions of one …

An essential step toward understanding neural circuits is linking their structure and their
dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical …

Approximate Message Passing algorithms for rotationally invariant matrices Page 1 The
Annals of Statistics 2022, Vol. 50, No. 1, 197–224 https://doi.org/10.1214/21-AOS2101 © …

Computational barriers to estimation from low-degree polynomials Page 1 The Annals of
Statistics 2022, Vol. 50, No. 3, 1833–1858 https://doi.org/10.1214/22-AOS2179 © Institute of …

A precise high-dimensional asymptotic theory for boosting and minimum-l1-norm
interpolated classifiers Page 1 The Annals of Statistics 2022, Vol. 50, No. 3, 1669–1695 …

We study the problem of estimating a rank-1 signal in the presence of rotationally invariant
noise--a class of perturbations more general than Gaussian noise. Principal Component …

We consider the problem of estimating a rank-$1 $ signal corrupted by structured rotationally
invariant noise, and address the following question:\emph {how well do inference algorithms …

We consider the problem of parameter estimation in a high-dimensional generalized linear
model. Spectral methods obtained via the principal eigenvector of a suitable data …

The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a
fundamental limit of the measurement precision of incompatible observables. Here it is …

A bstract We give a free probabilistic proposal to compute the fine-grained radiation entropy
for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang …