The symmetric exclusion process (SEP), where particles hop on a one-dimensional lattice with the restriction that there can only be one particle per site, is a paradigmatic model of interacting particle systems. Recently, it has been shown that the nature of the initial conditions—annealed or quenched—has a quantitative impact on the long-time properties of tracer diffusion. However, so far, the cumulant generating function in the quenched case was only determined in the low-density limit and for the specific case of a half-filled system. Here, we derive it in the opposite dense limit with quenched initial conditions. Importantly, our approach also allows us to consider the nonequilibrium situations of (i) a biased tracer in the SEP and (ii) a symmetric tracer in a step of density. In the former situation, we show that the initial conditions have a striking impact, and change the very dependence of the cumulants on the bias.

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• Random walks
• Exclusion processes