Related papers: Superdiffusive central limit theorem for a class o…
We study the continuum version of the dual theory for a system of two-dimensional, zero temperature, disordered bosons, interacting with short range repulsion and at a commensurate density. The dual theory, which describes vortices in the…
This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\Omega\subset\mathbb{R}^N$…
We consider stochastic wave equations in spatial dimensions $d \geq 4$. We assume that the driving noise is given by a Gaussian noise that is white in time and has some spatial correlation. When the spatial correlation is given by the Riesz…
We study McKean--Vlasov Stochastic Differential Equations (MV-SDEs) whose drift and diffusion coefficients are of superlinear growth in \textit{all} their variables thus also superlinear in the measure component (the meaning is specified in…
We present a comprehensive analysis of critical behavior in the driven-dissipative Bose condensation transition in three spatial dimensions. Starting point is a microscopic description of the system in terms of a many-body quantum master…
The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence. As a second main result, a…
In \cite{fgn1}, the hydrodynamic limit in the diffusive scaling of the symmetric simple exclusion process with a finite number of slow bonds of strength $n^{-\beta}$ has been studied. Here $n$ is the scaling parameter and $\beta>0$ is…
In this paper, we investigate generalized Carleman kinetic equation for n$\ge$2 and prove convergence towards the solution of equation with fast diffusion or porous medium type, $u_t=\Delta u^m$ ($0\le m\le2$), in its diffusive hydrodynamic…
There has been a great deal of recent interest in learning and approximation of functions that can be expressed as expectations of a given nonlinearity with respect to its random internal parameters. Examples of such representations include…
This article is devoted to the numerical study of various finite difference approximations to the stochastic Burgers equation. Of particular interest in the one-dimensional case is the situation where the driving noise is white both in…
A diffusive stochastic Schr\"odinger equation (SSE) is shown for the first time, such that contributes to a non-completely positive dynamics. This contradicts to a recent Letter [arXiv:1303.4284] claiming that SSEs, under most general…
The Swift-Hohenberg equation (SHE) is a partial differential equation that explains how patterns emerge from a spatially homogeneous state. It has been widely used in the theory of pattern formation. Following a recent study by Bramburger…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We investigate a class of higher-order nonlinear dispersive equations posed on the circle, subject to additive forcing by a finite-dimensional control. Our main objective is to establish approximate controllability by using the…
The strong convergence of an explicit full-discrete scheme is investigated for the stochastic Burgers-Huxley equation driven by additive space-time white noise, which possesses both Burgers-type and cubic nonlinearities. To discretize the…
Finite difference/element/volume methods of discretising PDEs impose a subgrid scale interpolation on the dynamics. In contrast, the holistic discretisation approach developed herein constructs a natural subgrid scale field adapted to the…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…
We introduce the Stochastic Box-Ball System (SBBS), a probabilistic cellular automaton that generalizes the classic Takahashi-Satsuma Box-Ball System. In SBBS, particles are transported by a carrier with a fixed capacity that may fail to…
This paper considers a large class of nonlinear integro-differential scalar equations which involve an anomalous diffusion (e.g. driven by a fractional Laplacian) and a non-local singular convolution kernel. Each of those singular equations…
Let $d\geq 2$. In this paper, we investigate the following stochastic differential equation (SDE) in ${\mathbb R}^d$ driven by Brownian motion $$ {\rm d} X_t=b(t,X_t){\rm d} t+\sqrt{2}{\rm d} W_t, $$ where $b$ belongs to the space ${\mathbb…