2014/01/12 by Milton Jara, Jara, Milton
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #math.PR
paper · pdf · doi:10.48550/arxiv.1401.2609
arxiv created 2014/01/12 · openalex publication_date 2014/01/12 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.