Abstract
We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the $2$-point function of the two-dimensional Ising model. This factor was first computed by C. Tracy in \cite{T} via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom \cite{TW} using Fredholm determinant representations of the correlation function and Wiener-Hopf approximation results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlev\'e-III transcendent from \cite{MTW}.
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