Related papers: Rough Homogenisation with Fractional Dynamics

We show by means of experiments, theory and simulations, that the slow dynamics of coarsening systems displays dynamic heterogeneity similar to that observed in glass-forming systems. We measure dynamic heterogeneity via novel multi-point…

We establish a simultaneous generalization of It\^o's theory of stochastic and Lyons' theory of rough differential equations. The interest in such a unification comes from a variety of applications, including pathwise stochastic filtering,…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

We formulate and study a general family of (continuous-time) stochastic dynamics for accelerated first-order minimization of smooth convex functions. Building on an averaging formulation of accelerated mirror descent, we propose a…

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…

Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…

Generative diffusion models showed high success in many fields with a powerful theoretical background. They convert the data distribution to noise and remove the noise back to obtain a similar distribution. Many existing reviews focused on…

We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…

We address an original approach for the convergence analysis of a finite-volume scheme for the approximation of a stochastic diffusion-convection equation with multiplicative noise in a bounded domain of $\mathbb{R}^d$ (with $d=2$ or $3$)…

The long-time behavior of stochastic Hamilton-Jacobi equations is analyzed, including the stochastic mean curvature flow as a special case. In a variety of settings, new and sharpened results are obtained. Among them are (i) a…

In a stochastic process, where noise is always present, the fluctuation-dissipation theorem (FDT) becomes one of the most important tools in statistical mechanics and, consequently, it appears everywhere. Its major utility is to provide a…

Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…

We study the problem of lateral diffusion on a static, quasi-planar surface generated by a stationary, ergodic random field possessing rapid small-scale spatial fluctuations. The aim is to study the effective behaviour of a particle…

In this paper, we study a simple hydrodynamical model showing abrupt flow reversals at random times. For a suitable range of parameters, we show that the dynamics of flow reversal is accurately described by stochastic differential…

We investigate the existence of a robust, i.e., continuous, representation of the conditional distribution in a stochastic filtering model for multidimensional correlated jump-diffusions. Even in the absence of jumps, it is known that in…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [von Pezold et al, Physical Review B 2010; Wei et…

We establish the large deviation principle for the slow variables in slow-fast dynamical system driven by both Brownian noises and L\'evy noises. The fast variables evolve at much faster time scale than the slow variables, but they are…

Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This…

Homogenisation theory has seen recent applications in deriving stochastic transport models for fluid dynamics. In this work, we first derive the stochastic Lagrange-to-Euler map that underpins stochastic transport noise in fluid dynamics as…