We investigate contraction of the Wasserstein distances on $\mathbb{R}^d$ under Gaussian smoothing. It is well known that the heat semigroup is exponentially contractive with respect to the… Expand

We study the high-dimensional limit of the free energy associated with the inference problem of a rank-one nonsymmetric matrix. The matrix is expressed as the outer product of two vectors, not… Expand

This work shows that the limit free energy of the general statistical inference model of tensor products must be the viscosity solution to a certain Hamilton-Jacobi equation.Expand

The high-dimensional limit of the free energy associated with the inference problem of finite-rank matrix tensor products is studied and the limit is identified with the solution of a certain Hamilton-Jacobi equation.Expand

A pointed convex cone in a Hilbert space naturally induces a partial order, and further a notion of nondecreasingness for functions. We consider extended real-valued functions defined on the cone.… Expand

For a smooth vector field in a neighborhood of a critical point with all positive eigenvalues of the linearization, we consider the associated dynamics perturbed by white noise. Using Malliavin… Expand

We give an intrinsic meaning to the Hamilton–Jacobi equation arising from meanfield spin glass models in the viscosity sense, and establish the corresponding well-posedness. Originally defined on the… Expand

The high-dimensional limit of the free energy associated with a multi-layer generalized linear model is computed in terms of a variational formula whose initial condition is related to the limiting free energy of a model with one fewer layer.Expand

We consider exit problems for small white noise perturbations of a dynamical system generated by a vector field, and a domain containing a critical point with all positive eigenvalues of… Expand