Equilibrium fluctuations of asymmetric simple exclusion processes in dimension \(d\geq 3\) (Q5943924)

The authors consider an asymmetric exclusion process in dimension \(d\geq 3\) under diffusive rescaling starting from the Bernoulli product measure with density \(0<\alpha<1\). They prove the following main statement: For \(N\rightarrow\infty\) the corresponding fluctuation field \(Y_{t}^{N}\) converges to a generalized Ornstein-Uhlenbeck process \(Y_{t}\). The latter is a formal solution of the stochastic equation \(dY_{t}= \mathcal{A}Y_{t} dt + dB_{t}^{\nabla}\), where \(\mathcal{A}\) is a second order differential operator and \(B_{t}^{\nabla}\) is a mean zero Gaussian field with known covariance.