# Stationary states in infinite volume with non zero current

## TL;DR

This paper demonstrates the existence of stationary measures with non-zero current in infinite-volume Ginzburg-Landau stochastic models under specific geometries in three or more dimensions, without external forces.

## Contribution

It proves the existence of non-zero current stationary states in infinite-volume stochastic models without external forces, under certain geometric conditions.

## Key findings

- Existence of stationary measures with non-zero current in infinite domains.
- Non-zero current states occur without external forces in specific geometries.
- Results are valid in three or more dimensions.

## Abstract

We study the Ginzburg-Landau stochastic models in infinite domains with some special geometry and prove that without the help of external forces there are stationary measures with non zero current in three or more dimensions.