Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the
minimum of a set of random variables. This is an important problem for any time-series and …

Rich out-of-equilibrium collective dynamics of strongly interacting large assemblies emerge
in many areas of science. Some intriguing and not fully understood examples are the glassy …

Single-index models are a class of functions given by an unknown univariate``link''function
applied to an unknown one-dimensional projection of the input. These models are …

We focus on the task of learning a single index model $\sigma (w^\star\cdot x) $ with respect
to the isotropic Gaussian distribution in $ d $ dimensions. Prior work has shown that the …

We compute the typical number of equilibria of the generalized Lotka-Volterra equations
describing species-rich ecosystems with random, nonreciprocal interactions using the …

Inference problems with conjectured statistical-computational gaps are ubiquitous
throughout modern statistics, computer science, statistical physics and discrete probability …

We consider the problem of estimating a large rank‐one tensor u⊗ k∈(ℝn)⊗ k, k≥ 3, in
Gaussian noise. Earlier work characterized a critical signal‐to‐noise ratio λ Bayes= O (1) …

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising
in high-dimensional inference tasks. Here one produces an estimator of an unknown …

We study the algorithmic thresholds for principal component analysis of Gaussian k-tensors
with a planted rank-one spike, via Langevin dynamics and gradient descent. In order to …

We consider a nonlinear autonomous system of N≫ 1 degrees of freedom randomly
coupled by both relaxational (“gradient”) and nonrelaxational (“solenoidal”) random …