Related papers: The mean field Schr\"odinger problem: ergodic beha…
In this article we investigate entropic interpolations. These measure valued curves describe the optimal solutions of the Schr{\"o}dinger problem [Sch31], which is the problem of finding the most likely evolution of a system of independent…
We consider the problem to identify the most likely flow in phase space, of (inertial) particles under stochastic forcing, that is in agreement with spatial (marginal) distributions that are specified at a set of points in time. The…
Mean-Field Game (MFG) serves as a crucial mathematical framework in modeling the collective behavior of individual agents interacting stochastically with a large population. In this work, we aim at solving a challenging class of MFGs in…
We consider the mean field Fokker-Planck equation subject to nonlinear no-flux boundary conditions, which necessarily arise when subjecting a system of Brownian particles interacting via a pair potential in a bounded domain. With the…
In this work, we study the mean field Schr\"odinger problem from a purely probabilistic point of view by exploiting its connection to stochastic control theory for McKean-Vlasov diffusions. Our main result shows that the mean field…
We develop a perturbative framework to calculate the mean-squared displacement (MSD) of active Brownian particles (ABPs) with a finite moment of inertia. Starting from the corresponding Fokker-Planck equation, we employ a Fourier transform…
We develop novel numerical methods and perturbation approaches to determine the mean first passage time (MFPT) for a Brownian particle to be captured by either small stationary or mobile traps inside a bounded 2-D confining domain. Of…
We study the problem of optimal control for mean-field stochastic partial differential equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in the case of \textit{partial…
We formulate and investigate a mean field optimization (MFO) problem over a set of probability distributions $\mu$ with a prescribed marginal $m$. The cost function depends on an aggregate term, which is the expectation of $\mu$ with…
A Schr\"odinger bridge is the most probable time-dependent probability distribution that connects an initial probability distribution $w_{i}$ to a final one $w_{f}$. The problem has been solved and widely used for the case of simple…
Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by adding the Fisher Information as the regularizer, we relate the…
There has been recent interest in the relaxational modes of small-scale fully connected systems of aligning self-propelled particles (Spera et al., Phys. Rev. Lett. {\bf 132}: 078301 (2024)). We revisit the classical connection between…
E. Schroedinger proposed the equation to find the statistical property of a quantum particle on a finite time interval. It is called "Schroedinger's functional equation". Given probability distributions of a particle at initial and terminal…
The \emph{Schr\"odinger problem} is obtained by replacing the mean square distance with the relative entropy in the Monge-Kantorovich problem. It was first addressed by Schr\"odinger as the problem of describing the most likely evolution of…
We study the long-range asymptotic behavior for an out-of-equilibrium countable one-dimensional system of Brownian particles interacting through their rank-dependent drifts. Focusing on the semi-infinite case, where only the leftmost…
We study stochastic evolution equations describing the dynamics of open quantum systems. First, using resolvent approximations, we obtain a sufficient condition for regularity of solutions to linear stochastic Schroedinger equations driven…
Motivated by continuous-time optimal inventory management, we study a class of stationary mean-field control problems with singular controls. The dynamics are modeled by a mean-reverting Ornstein-Uhlenbeck process, and the performance…
We analyze the mean-field limit of a stochastic Schr{\"o}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described…
Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a…
We study the convergence problem of mean-field control theory in the presence of state constraints and non-degenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems…