Related papers: On the "Matrix Approach" to interacting particle s…
Consider a rectangular matrix describing some type of communication or transportation between a set of origins and a set of destinations, or a classification of objects by two attributes. The problem is to infer the entries of the matrix…
We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a switched random process to keep closer to equilibrium at each time, thanks…
Enzymatic molecules that actively support many cellular processes, including transport, cell division and cell motility, are known as motor proteins or molecular motors. Experimental studies indicate that they interact with each other and…
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…
We provide estimation methods for nonseparable panel models based on low-rank factor structure approximations. The factor structures are estimated by matrix-completion methods to deal with the computational challenges of principal component…
The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of $n$ sites. It is partially…
We present an approach to the dynamics of interacting particle systems, which allows to derive path integral formulas from purely stochastic considerations. We show that the resulting field theory is a dual version of the standard theory of…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us…
We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the leading singularities of the operator…
In these lecture we explain why limiting distribution function, like the Tracy-Widom distribution, or limit processes, like the Airy_2 process, arise both in random matrices and interacting particle systems. The link is through a common…
The model of the physical system with discrete interactions is based on the postulates that (i) parameters of the physical system are defined in process of its interaction; (ii) the process of interaction is discrete. Consequently ordering…
We derive a formula for the quasi-potential of one-dimensional symmetric exclusion process in weak contact with reservoirs. The interaction with the boundary is so weak that, in the diffusive scale, the density profile evolves as the one of…
In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix $A \in \mathbb{R}^{m \times n}$ with $m < n$, by a partial circulant matrix with rows related by…
A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the…
We present a solution for the stationary state of an asymmetric exclusion model with sequential update and open boundary conditions. We solve the model exactly for random hopping in both directions by applying a matrix-product formalism…
We study a two-species partially asymmetric exclusion process where the left boundary is permeable for the `slower' species but the right boundary is not. We find a matrix product solution for the stationary state, and the exact stationary…
Interacting particle systems are continuous time Markov processes which are used to construct models in many disciplines. Monotonicity is a property that some interacting particle systems possess. A monotone interacting particle system is…
Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…