Quadratic Fluctuations of the Simple Exclusion Process
Probability
2014-01-14 v1 Statistical Mechanics
Mathematical Physics
math.MP
Abstract
We introduce a two-dimensional, distribution-valued field which we call the quadratic field associated to the one-dimensional Ornstein-Uhlenbeck process. We show that the stationary quadratic fluctuations of the simple exclusion process, when rescaled in the diffusive scaling, converge to this quadratic field. We show that this quadratic field evaluated at the diagonal corresponds to the Wick-renormalized square of the Ornstein-Uhlenbeck process, and we use this new representation in order to prove some small and large-time properties of it.
Keywords
Cite
@article{arxiv.1401.2609,
title = {Quadratic Fluctuations of the Simple Exclusion Process},
author = {Milton Jara},
journal= {arXiv preprint arXiv:1401.2609},
year = {2014}
}