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 v_q an ergodic component of the reversible Bernoulli product measure which places a particle at x with probability q^x/(1 + q^x). It is well known that under some hypotheses on a local function V, (1/√t) ∫₀^t V(η_s) 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).