| Abstract: |
| We consider a class of particle systems with local interactions in continuous space, which
are reversible with respect to the Poisson measures with constant density. A natural
quantity of interest capturing the large-scale behavior of particles in this set-up is the
bulk diffusion matrix. Recent work by Giunti, Gu, and Mourrat has established that
finite-volume approximations of this diffusion matrix converge at an algebraic rate. We
show that the bulk diffusion matrix is an infinitely differentiable function of the density
of particles, and obtain relatively explicit expressions for the derivatives in terms of the
corrector, an object which already appeared in the description of the bulk diffusion matrix itself.
Based on joint work with Giunti, Gu, and Mourrat. |
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