3 problems

Consider the density fluctuation field for the one-dimensional asymmetric simple exclusion process in the longer time scale, after subtracting the velocity of the system. Static de…

Let $k$ be a positive integer, let $t$ denote time, and let $x_1,x_2,\dots,x_k$ be spatial variables. For each $j$, let ${\mathcal X}^{(j)}_t$ denote the $j$th-order fluctuation fi…

Let $\mathcal{Y}^n$ be the field considered above, with time scale $\theta(n)=n^a$, and let $\kappa$ be the parameter governing the model. The first item of the preceding theorem a…