Statistics of small length scale density fluctuations in supercooled viscous liquids

Many successful theories of liquids near the melting temperature assume that small length scale density fluctuations follow Gaussian statistics. In this paper I present numerical investigations of fluctuations in the supercooled viscous regime using an enhance sampling method. I present results for the single component Lennard-Jones liquid, the Kob-Andersen binary mixture, the Wahnstr\"om binary mixture, the Lewis-Wahnstr\"om model of ortho-terphenyl and for the TIP4P/Ice model of water. Results show that the Gaussian approximation persist to a good degree into the supercooled viscous regime, however, the approximation is less accurate at low temperatures. I relate the non-Gaussian fluctuations to crystalline configurations. Implications to theories of the glass transition are discussed.