Related papers: Spontaneous stochasticity and renormalization grou…
We consider the long time statistics of a one-dimensional stochastic Ginzburg-Landau equation with cubic nonlinearity while being subjected to random perturbations via an additive Gaussian noise. Under the assumption that sufficiently many…
We consider a statistical limit of solutions to the compressible Navier--Stokes system in the high Reynolds number regime in a domain exterior to a rigid body. We investigate to what extent this highly turbulent regime can be modeled by an…
This paper deals with the stochastic control of nonlinear systems in the presence of state and control constraints, for uncertain discrete-time dynamics in finite dimensional spaces. In the deterministic case, the viability kernel is known…
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. This…
This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing,…
It is well-known that the fundamental diagram in a realistic traffic system is featured by capacity drop. From a mesoscopic approach, we demonstrate that such a phenomenon is linked to the unique properties of stochastic noise, which, when…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
We consider the symmetric simple exclusion process in $\mathbb Z^d$ with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process,…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
Quantifying energy flows at nanometer scales promises to guide future research in a variety of disciplines, from microscopic control and manipulation, to autonomously operating molecular machines. A general understanding of the…
A dyadic shell model for the Navier-Stokes equations is studied in the context of turbulence. The model is an infinite nonlinearly coupled system of ODEs. It is proved that the unique fixed point is a global attractor, which converges to…
We survey the recent advance in the rigorous qualitative theory of the 2d stochastic Navier-Stokes system that are relevant to the description of turbulence in two-dimensional fluids. After discussing briefly the initial-boundary value…
Recently, a concept of deterministic and stochastic turbulence has been introduced based on experiments with a boundary layer. In these experiments, the flow was driven with controlled random perturbation; in addition, natural ambient noise…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
In this paper we study a stochastic version of an inviscid shell model of turbulence with multiplicative noise. The deterministic counterpart of this model is quite general and includes inviscid GOY and Sabra shell models of turbulence. We…