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Space-time fluctuations in a quasi-static limit

C. Bernardin, P. Gonçalves, S. Olla

Abstract

We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space.

Space-time fluctuations in a quasi-static limit

Abstract

We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space.
Paper Structure (9 sections, 4 theorems, 98 equations)

This paper contains 9 sections, 4 theorems, 98 equations.

Table of Contents

  1. Introduction
  2. SSEP with boundary reservoirs
  3. The model
  4. Hydrodynamic limit
  5. Main result
  6. Proof of Theorem \ref{['th:mainthm1']}
  7. Convergence of finite-dimensional distributions
  8. Tightness
  9. Generalization and discussion

Key Result

Theorem 1

The sequence $\{\mathbb Y^N \; ; \; N\ge 1\}$ converges in law, as $N\to+\infty$, to $\mathbb Y$.

Theorems & Definitions (8)

  • Theorem 1
  • Remark 1
  • Proposition 1
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof