Related papers: Gaussian theory for spatially distributed self-pro…
We consider a toy model for glassy dynamics of colloidal suspensions: a single Brownian particle diffusing among immobile obstacles. If Gaussian factorization of static density fluctuations is assumed, this model can be solved without…
We consider a system of $N$ disordered mean-field interacting diffusions within spatial constraints: each particle $\theta_i$ is attached to one site $x_i$ of a periodic lattice and the interaction between particles $\theta_i$ and…
Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…
Using the path integral approach, we obtain the characteristic functions of the gyration radius distributions for Gaussian star and Gaussian rosette macromolecules. We derive the analytical expressions for cumulants of the both…
In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
Computing the posterior distribution of a probabilistic program is a hard task for which no one-fit-for-all solution exists. We propose Gaussian Semantics, which approximates the exact probabilistic semantics of a bounded program by means…
The overdamped Brownian motion of a self-propelled particle which is driven by a projected internal force is studied by solving the Langevin equation analytically. The "active" particle under study is restricted to move along a linear…
Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation…
Working with a toy model whose partition function consists of a discrete summation, we introduce the statistical field-theory methodology by transforming a partition function via a formal Gaussian integral relation (the Hubbard-Stratonovich…
We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…
We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly…
First principles simulations of the quantum dynamics of interacting Bose gases using the stochastic gauge representation are analyzed. In a companion paper, we showed how the positive P representation can be applied to these problems using…
The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes,…
Paths of particles, emitted from distributed sources and passing out through slits of two gratings, $G_{0}$ and $G_{1}$, up to detectors, have been computed in details by the path integral method. The slits are represented by Gaussian…
We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…
We consider a system of interacting particles with random initial conditions. Continuum approximations of the system, based on truncations of the BBGKY hierarchy, are described and simulated for various initial distributions and types of…
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
We study a one-dimensional system of spatially extended particles, which are fixated to regularly spaced locations by means of elastic springs. The particles are assumed to be driven by a Gaussian noise and to have dissipative,…