Abstract
The normalization of Bethe eigenstates for the totally asymmetric simple exclusion process on a ring of \(L\) sites is studied, in the large \(L\) limit with finite density of particles, for all the eigenstates responsible for the relaxation to the stationary state on the KPZ time scale \(T\sim L^{3/2}\). In this regime, the normalization is found to be essentially equal to the exponential of the action of a scalar free field. The large \(L\) asymptotics is obtained using the Euler–Maclaurin formula for summations on segments, rectangles and triangles, with various singularities at the borders of the summation range.
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