  For diffusive many-particle systems such as the SSEP (symmetric simple
exclusion process) or independent particles coupled with reservoirs at the
boundaries, we analyze the density fluctuations conditioned on current
integrated over a large time. We determine the conditioned large deviation
function of density by a microscopic calculation. We then show that it can be
expressed in terms of the solutions of Hamilton-Jacobi equations, which can be
written for general diffusive systems using a fluctuating hydrodynamics
description.
