I'll try to find some links for you when I am not watching the kids and my work deadline is fulfilled, but the short version is that DNA analysis shows little if any Central Asian ancestry in modern Jews, but does show common Mideastern ancestry among both Sephardic and Ashkenazi groups, along with an average of around 40% European admixture. There is one Jewish scientist who disagrees, I forget his name at the moment, but almost no one else takes him seriously except some Christian Identity folks who desperately want the latest findings to go away.

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To clarify: This doesn't mean that zero conversions occurred. It just means it wasn't a statistically large number. And it does mean that the claim all Ashkenazis are really Khazars and have no Middle Eastern ancestry is definitely false.