Abstract
The joint probability distribution function (PDF) of the height and its gradients is derived for a zero tension d + 1-dimensional Kardar-Parisi-Zhang (KPZ) equation. It is proved that the height's PDF of zero tension KPZ equation shows lack of positivity after a finite time t c . The properties of zero tension KPZ equation and its differences with the case that it possess an infinitesimal surface tension is discussed. Also potential relation between the time scale t c and the singularity time scale t c.v→0 of the KPZ equation with an infinitesimal surface tension is investigated.
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Bahraminasab, A., Tabei, S.M.A., Masoudi, A.A. et al. Zero Tension Kardar-Parisi-Zhang Equation in (d + 1)–Dimensions. Journal of Statistical Physics 116, 1521–1544 (2004). https://doi.org/10.1023/B:JOSS.0000041747.55551.8b
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DOI: https://doi.org/10.1023/B:JOSS.0000041747.55551.8b