Regularity of diffusion coefficient for nearest neighbor asymmetric simple exclusion on Z

We consider the nearest neighbor asymmetric exclusion process on Z, in which particles jump with probability p(1) to the right and p(-1) to the left. Let q=p(1)/p(-1) and denote by νq an ergodic component of the reversible Bernoulli product measure which places a particle at x with probability qx/(1+qx). It is well known that under some hypotheses on a local function V, (1/t)∫0tV(ηs)ds converges to a normal distribution with variance σ2=σ2(q), which depends on q. We prove in this article that σ2(q) is a C∞ function of q on (0,1).