Symmetric simple exclusion process: Regularity of the self-diffusion coefficient. (English) Zbl 0994.60093

Landim, C.; Olla, S.; Varadhan, S. R. S.

Commun. Math. Phys. 224, No. 1, 307-321 (2001).

Summary: We prove that the self-diffusion coefficient of a tagged particle in the symmetric exclusion process in \(Z^d\), which is in equilibrium at density \(\alpha\), is of class \(C^\infty\) as a function of \(\alpha\) in the closed interval \([0,1]\). The proof provides also a recursive method to compute the Taylor expansion at the boundaries.

MSC:

60K35

Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

self-diffusion coefficient; equilibrium at density; Taylor expansion at the boundaries