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This paper focuses on stochastic saddle point problems with decision-dependent distributions. These are problems whose objective is the expected value of a stochastic payoff function and whose data distribution drifts in response to…
High-dimensional networks producing oscillatory dynamics are ubiquitous in biological systems. Unravelling the mechanism of oscillatory dynamics in biological networks with stochastic perturbations becomes paramountly significant. Although…
Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…
The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a…
In BP models with hundreds of fluxes, we compute the effects of cosmological dynamics on the probability distribution of landscape vacua. Starting from generic initial conditions, we find that most fluxes are dynamically driven into a…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
Self-gravitating system are non-equilibrium a priory. A new approach is proposed, which employs a non-equilibrium statistical operator into account inhomogeneous distribution of particles and temperature. The method involves the saddle -…
In this paper, we present a fine-grained analysis of the local landscape of phase retrieval under the regime of limited samples. Specifically, we aim to ascertain the minimal sample size required to guarantee a benign local landscape…
Eigenvalue distributions are important dynamical quantities in matrix models, and it is a challenging problem to derive them in tensor models. In this paper, we consider real symmetric order-three tensors with Gaussian distributions as the…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
This work is concerned with approximating the smallest eigenvalue of a parameter-dependent Hermitian matrix $A(\mu)$ for many parameter values $\mu \in \mathbb{R}^P$. The design of reliable and efficient algorithms for addressing this task…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
We prove that in dimension one the non-real eigenvalues of the non-Hermitian Anderson (NHA) model with a selfaveraging potential are regularly spaced. The class of selfaveraging potentials which we introduce in this paper is very wide and…
Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the…
State-specific approximations can provide an accurate representation of challenging electronic excitations by enabling relaxation of the electron density. While state-specific wave functions are known to be local minima or saddle points of…
We investigate the convergence of McKean-Vlasov diffusions in a nonconvex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures…
We obtain a tail bound for the least non-zero singular value of $A-z$ when $A$ is a random matrix and $z$ is an eigenvalue of $A$ in a neighbourhood of a given point $z_0$ in the bulk of the spectrum. The argument relies on a resolvent…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…