THE HOLOCAUST: Does Judaism Believes in Gilgul? Transmigrations of Souls

Does Judaism believe in reincarnation? Is there a soul that outlives the body? Could that soul come back to a new body carrying the memories of the former? Are there people who beleive they died in the Holocaust and are reincarnated? Is there any evidence that makes reincarnation not only plausible but likely? While some authorities, such as Saadia Gaon (10th century) denied reincarnation as a Jewish concept, from the 17th century onward, leading rabbis of normative Judaism, such as the Gaon of Vilna and the Chafetz Chaim 2, referred to gilgul neshamot as a fact