Related papers: On the relation between gradient flows and the lar…
We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial…
Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clumping in colloid dispersions. Our model is stochastic but rigorously derived from a deterministic setup…
We study the large deviation behavior of a system of diffusing particles with a mean field interaction, described through a collection of stochastic differential equations, in which each particle is driven by a vanishing independent…
In finite dimension, the long-time and metastable behavior of a gradient flow perturbated by a small Brownian noise is well understood. A similar situation arises when a Wasserstein gradient flow over a space of probability measure is…
We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the limit of approximations constructed via a deterministic…
Let $\sigma(u)$, $u\in \mathbb{R}$ be an ergodic stationary Markov chain, taking a finite number of values $a_1,...,a_m$, and $b(u)=g(\sigma(u))$, where $g$ is a bounded and measurable function. We consider the diffusion type process $$…
Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
The large deviation function for entropy production is calculated for a particle driven along a periodic potential by solving a time-independent eigenvalue problem. In an intermediate force regime, the large deviation function shows…
We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…
Employing large deviation theory, we explore current fluctuations of underdamped Brownian motion for the paradigmatic example of a single particle in a one dimensional periodic potential. Two different approaches to the large deviation…
We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geometric structure of the gradient flows in two instances,…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…
Motivated by policy gradient methods in the context of reinforcement learning, we identify a large deviation rate function for the iterates generated by stochastic gradient descent for possibly non-convex objectives satisfying a…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
In this paper we consider a nonlinear Fokker-Planck equation with asymptotically small parameters. It describes the diffusion of finite-size particles in the presence of a fixed distribution of obstacles in the limit of low-volume fraction.…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert particle increases due to the influence of an external…
We propose a derivation of a nonequilibrium Langevin dynamics for a large particle immersed in a background flow field. A single large particle is placed in an ideal gas heat bath composed of point particles that are distributed…
Given a particle system obeying overdamped Langevin dynamics, we demonstrate that it is always possible to construct a thermodynamically consistent macroscopic model which obeys a gradient flow with respect to its non-equilibrium free…