相关论文: Transportation to random zeroes by the gradient fl…

We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…

Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a…

The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…

In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…

We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pairs that are out of sort with respect to the initial…

The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…

We consider a stochastic process in which independent identically distributed random matrices are multiplied and where the Lyapunov exponent of the product is positive. We continue multiplying the random matrices as long as the norm,…

This is the first of a series of papers devoted to a thorough analysis of the class of gradient flows in a metric space $(X,\mathsf{d})$ that can be characterized by Evolution Variational Inequalities. We present new results concerning the…

Surface transport of inertial particles is investigated by means of the perturbative approach, introduced by Maxey (J. Fluid Mech. 174, 441 (1987)), which is valid in the case the deflections induced on the particle trajectories by the…

We consider the paths of a Gaussian random process $x(t)$, $x(0)=0$ not exceeding a fixed positive level over a large time interval $(0,T)$, $T\gg 1$. The probability $p(T)$ of such event is frequently a regularly varying function at…

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…

Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…

We introduce an optimal transport topology on the space of probability measures over a fiber bundle, which penalizes the transport cost from one fiber to another. For simplicity, we illustrate our construction in the Euclidean case…

This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss…

Transport of spherical Brownian particles of finite size possessing radii through narrow channels with varying cross-section area is considered. Applying the so-called Fick-Jacobs approximation, i.e. assuming fast equilibration in…

Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…

We study when a given Gaussian random variable on a given probability space $(\Omega, {\cal{F}}, P) $ is equal almost surely to $\beta_{1}$ where $\beta $ is a Brownian motion defined on the same (or possibly extended) probability space. As…

We study statistical properties of two-dimensional turbulent flows. Three systems are considered: the Navier-Stokes equation, surface quasi-geostrophic flow, and a model equation for thermal convection in the Earth's mantle. Direct…

We generate random functions locally via a novel generalization of Dyson Brownian motion, such that the functions are in a desired differentiability class, while ensuring that the Hessian is a member of the Gaussian orthogonal ensemble…

We analyze the gradient flow of a potential energy in the space of probability measures when we substitute the optimal transport geometry with a geometry based on Sinkhorn divergences, a debiased version of entropic optimal transport. This…