Regularity of diffusion coefficient for nearest neighbor asymmetric simple exclusion on

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 ν 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 ) d s converges to a normal distribution with variance σ 2 = σ 2 ( q ) , which depends on q. We prove in this article that σ 2 ( q ) is a C ∞ function of q on ( 0 , 1 ) .