a. Khazar theory is bullshit and has been thoroughly debunked. b. Mizrahim are almost entirely descended from Israelites (probably some admixture with local non Jews over the years but minimal). c. Ashkenazim are predominantly of Levantine/Israelite origins with most of their admixture on their mtDNA. This is probably because the Romans would have kept Judean women for themselves and eventually bred them out of existence whilst keeping the men as slaves. The men would have had to have picked up local Roman women to continue to breed. Also some of the men would have been traders prior to the Roman exile who would have picked up some women along the way, plus there was also a community of Jews that left Israel because of the Ptolemaic vs Selecuid turmoil earlier. Some of the Ashkenazi mtDNA lineages however (such as the K lineages that were originally assigned as European) have been re-assigned as Middle Eastern based on Syrian PPNB samples. d. Ethiopian/Indian Jews have a small amount of Y-DNA tracing back to the Levant but they are of local populations.