相关论文: Stochastic Master Fields
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We propose an efficient way to sample from a class of structured multivariate Gaussian distributions which routinely arise as conditional posteriors of model parameters that are assigned a conditionally Gaussian prior. The proposed…
We propose a piecewise deterministic Markovian jump process in Hilbert space such that the covariance matrix of this stochastic process solves the thermodynamic quantum master equation. The proposed stochastic process is particularly simple…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument which is based only on the subadditive structure of maximal subsolutions (solutions of the "metric problem"). This permits us to give…
We derive a quantum master equation in the context of a polymerized open quantum mechanical system for the scattering of a Brownian particle in an ideal gas environment. The model is formulated in a top-down approach by choosing a…
Forest transitions, characterized by dynamic shifts between forest, agricultural, and abandoned lands, are complex phenomena. This study developed a stochastic differential equation model to capture the intricate dynamics of these…
We introduce a new numerical algorithm for solving the stochastic neural field equation (NFE) with delays. Using this algorithm we have obtained some numerical results which illustrate the effect of noise in the dynamical behaviour of…
A systematic first-order correction to the standard Markov master equation for open quantum systems interacting with a bosonic bath is presented. It extends the Markov Lindblad master equation to the more general case of non-Markovian…
Bosonic mean-field theories can approximate the dynamics of systems of $n$ bosons provided that $n \gg 1$. We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions…
In this paper, we connect some recent papers on smoothing of energy landscapes and scored-based generative models of machine learning to classical work in stochastic control. We clarify these connections providing rigorous statements and…
In this paper we consider an alternative formulation of a class of stochastic wave and master equations with scalar noise that are used in quantum optics for modelling open systems and continuously monitored systems. The reformulation is…
A nonlinear master equation is derived, reflecting properly the entropy of open quantum systems. In contrast to linear alternatives, its equilibrium solution is exactly the canonical Gibbs density matrix. The corresponding nonlinear…
We study a simple model of the stochastic information filtering, in a randomly organized information system. For simplest versions of the model it appears to be possible to describe the filtering dynamics in terms of the master equations.…
Intrinsic Gaussian fields are used in many areas of statistics as models for spatial or spatio-temporal dependence, or as priors for latent variables. However, there are two major gaps in the literature: first, the number and flexibility of…
Stochastic solutions are obtained for the Maxwell-Vlasov equation in the approximation where magnetic field fluctuations are neglected and the electrostatic potential is used to compute the electric field. This is a reasonable approximation…
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels…
Motivated by current interest in understanding statistical properties of random landscapes in high-dimensional spaces, we consider a model of the landscape in $\mathbb{R}^N$ obtained by superimposing $M>N$ plane waves of random wavevectors…
Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. Here we first identify the rate constant limits under which the concentrations of a given set of species will tend to…
Using the Batalin-Vilkovisky formalism we provide a detailed analysis of the NS sector of boundary superstring field theory. We construct explicitly the relevant BV structure and derive the master action. Furthermore, we show that this…