This is a weird theory but in a way it makes perfect sence, Min, Aviendha and Elayne are all the split reincarnation of Ilyena. Let me explain, this first came to me when reading winters heart for the first time. During the chapter when the girls bond Rand their are constant references between the likeness of min and Aviendha, the same crossed arms and stance when talking to Rand, the same reaction to Rands attempted "escape".

This likeness is no accident, RJ goes to great lengths to make this show, and considering the completely different personalities and backgrounds that they come from, this cannot just be freek of nature. Also their is precedence for manarisms to be passed on to the new version, Rands stroaking of his ear when admiring women is said to be LTTs manirism.

Also this tri nature of the girls would explain why rand loves them the exactly, when he has completely different experinces of them, elayne had only few kisses for 4 days to get rands love while min and aviendha had months to make him "theirs". Also it would explain the rediculassly fast pace with which the girls fall in love with him, it takes elayne only seconds when he falls down on her and mni falls as quickly in her first encounter with him outside the inn. Also the very fact that the girls are willing to share him is evidence, not many women are willing to share!

Also i think this truth is important for the lews side of rand to rediscover itd sanity, which i think is a requirement for rands success.