Strong hydrodynamic limit for attractive particle systems on Z

TL;DR

This paper establishes almost sure Euler hydrodynamics for a broad class of attractive particle systems on the integer lattice, extending previous results with a novel constructive approach that bypasses traditional subadditive ergodic techniques.

Contribution

It introduces a new constructive method to prove hydrodynamic limits for attractive particle systems, generalizing earlier work and overcoming limitations of existing ergodic theorems.

Findings

Proves almost sure Euler hydrodynamics for various particle systems

Develops a new approach independent of subadditive ergodic theorem

Extends previous hydrodynamic limit results to broader settings

Abstract

We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on $\Z$ starting from an arbitrary initial profile. We generalize earlier works by Sepp\"al\"ainen (1999) and Andjel et al. (2004). Our constructive approach requires new ideas since the subadditive ergodic theorem (central to previous works) is no longer effective in our setting.