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We consider the asymmetric simple exclusion processes (ASEP) on a ringconstrained to produce an atypically large flux, or an extreme activity. Usingquantum free fermion techniques we find the time-dependent conditionaltransition probabilities and the exact dynamical structure factor under suchconditioned dynamics. In the thermodynamic limit we obtain the explicit scalingform. This gives a direct proof that the dynamical exponent in the extremecurrent regime is $z=1$ rather than the KPZ exponent $z=3/2$ whichcharacterizes the ASEP in the regime of typical currents. Some of our resultsextend to the activity in the partially asymmetric simple exclusion process,including the symmetric case.

Transition probabilities and dynamic structure factor in the ASEP conditioned on strong flux