Anatoly, You're right--3 dimensions ruins my symmetry argument. My mistake. On the other hand, I still suspect that there exists a realistic case where forcing the third cumulant to zero cause a much smaller increase in chi-square than forcing the fourth cumulant to zero; e.g., a broad, flat radial distribution function. For those of you out there who are relative novices, this is an entertaining and informative discussion, but I don't want to lose track of the practical point: It is very rare to find a system where the fourth cumulant is both necessary and sufficient. Either the potentials are close enough to harmonic that the fourth cumulant makes little difference, or they are so far from harmonic that the fourth cumulant alone is not enough. --Scott Calvin Sarah Lawrence College On Jan 21, 2009, at 10:11 PM, Frenkel, Anatoly wrote:
Thus, I am pretty much convinced, unless there is some mistake in my reasoning, that no case exists in 3D with a zero third cumulant.