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The Symmetric Exclusion Process (SEP), where particles hop on a 1D latticewith the restriction that there can only be one particle per site, is aparadigmatic model of interacting particle systems. Recently, it has been shownthat the nature of the initial conditions - annealed or quenched - has aquantitative impact on the long-time properties of tracer diffusion. However,so far, all the studies in the quenched case focused on the low-density limitof the SEP. Here, we derive the cumulant generating function of the tracerposition in the dense limit with quenched initial conditions. Importantly, ourapproach also allows us to consider the nonequilibrium situations of (i) abiased tracer in the SEP and (ii) a symmetric tracer in a step of density. Inthe former situation, we show that the initial conditions have a strikingimpact, and change the very dependence of the cumulants on the bias.

Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes