Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems

Hydrodynamics for a non-conservative Interacting Particle System

We obtain the hydrodynamic limit of one-dimensional interacting particle systems describing the macroscopic evolution of the density of mass in infinite volume from the microscopic dynamics. The processes are weak pertubations of the symmetric exclusion process by shift operators describing the spread of particles around positions where new sites are created.

Hydrodynamic limits for long-range asymmetric interacting particle systems

We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on ${\mathbb Z}^n$, where the jump rates are asymmetric and long-range of order $\|x\|^{-(n+α)}$ for a particle displacement of order $\|x\|$. Two types of evolution equations are identified depending on the strength of the long-range asymmetry. When $0<α<1$, we find a new integro-partial differential hydrodynamic equation, in an anomalous space-time scale. On the other hand, when $α\geq 1$, we derive a Burgers hydrodynamic equation, as in the fini…

Interacting particle systems: hydrodynamic limit versus high density limit

In this short survey we compare aspects of two different approaches for scaling limits of interacting particle systems, the hydrodynamic limit and the high density limit. We present some examples, comments and open problems on each approach for different scenarios: the law of large numbers, the central limit theorem, and the large deviations principle. It is given a special attention to a recent result of Franco and Groisman' 12 about the high density limit of a system exhibiting explosion of the total numbers of particles in finite time.

Hydrodynamic limits of interacting particle systems on crystal lattices in periodic realizations

We study the hydrodynamic limits of the simple exclusion processes and the zero range processes on crystal lattices. For a periodic realization of crystal lattice, we derive the hydrodynamic limit for the exclusion processes and the zero range processes, which depends on both the structure of crystal lattice and the periodic realization. Even through the crystal lattices have inhomogeneous local structure, for all periodic realizations, we apply the entropy method to derive the hydrodynamic limits. Also, we discuss how the limit equation depends on the choices of the realizations.

稀疏图上的一类相互作用跳跃过程流体动力学极限的可处理描述

Tractable description of hydrodynamic limits of a class of interacting jump processes on sparse graphs

本文针对稀疏随机图上的马尔可夫相互作用跳跃过程，在单粒子转移无环假设下，用有限耦合常微分方程组给出邻域经验测度流体动力学极限的可处理描述，并通过模拟验证其近似效果。

具有长程跳跃的对称包含过程的流体动力学极限与非平衡涨落

Hydrodynamic limits and non-equilibrium fluctuations for the Symmetric Inclusion Process with long jumps

本文研究允许任意长程跳跃的 d 维 SIP，利用自对偶性与 Dirichlet 形式 Mosco 收敛证明其经验测度满足非局部流体动力学方程，且密度涨落收敛为非局部广义 Ornstein–Uhlenbeck 过程。