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Employing the formalism introduced by Sinai and Yakhot [PRL, 63(18), p. 1962,1989], we study the probability density functions (pdf's) of decaying passivescalars in periodic domains under the influence of smooth large scale velocityfields. The particular regime we focus on is one where the normalized scalarpdf's attain a self-similar profile in finite time, i.e., the so called strangeor statistical eigenmode regime. In accordance with the work of Sinai andYakhot, the central regions of the pdf's are power laws. But the details of thepdf profiles are dependent on the physical parameters in the problem.Interestingly, for small Peclet numbers the pdf's {\it resemble} stretched orpure exponential functions, whereas in the limit of large Peclet numbers, thereemerges a universal Gaussian form for the pdf. Numerical simulations are usedto verify these predictions.Comment: 10 pages, 8 figs. To be submitted to PR

Probability density functions of decaying passive scalars in periodic domains: An application of Sinai-Yakhot theory