Randvér or Randver was, according to Sogubrot and the Lay of Hyndla, the son of Raodbardr or Radbard. the king of Gardariki (Nordic term for Rus which became Russia) and Aour the Deep Minded, the daughter of Ivar Vidfamne. In these two sources, Aour had Randver's brother, Harald Wartooth, in a previous marriage.
Hversu Noregr Byggoist (How Norway was inhabited) says he is the son of Hroerekr slongvanbaugi and the brother of Harald Wartooth.
On the other hand, according to the Hervarar saga, both Ranver and Harald Wartooth were the sons of Valdar and Alfhild, the daughter of Ivar Vidfamne. This saga relates that Ivar appointed Valdar the king of Denmark, and when Valdar died, he was succeeded by Randver. When his brother Harald, had reclaimed Gotaland or Gotland, Randver died hastily in England, and was succeeded by Sigurd Ring as the king of Denmark.
He was married to Ingild, the daughter of an unknown Swedish king. He was succeeded by his son Sigurd Ring.
Aour the deep minded, was apparently used by her father for political reasons. She was given to a Hroerekr slongvanbaugi, the king of Zealand, but preferred his brother Helgi the Sharp. Her father Ivar Vidfamne solved the problem by telling Hroerekr that she had been unfaithful with Helgi. Hroerekr killed his brother, afterwards it was easy for Ivar to attack Hroerekr and kill him as well.
She fled to Gardariki with her son Harold Wartooth, and married Radbardr and had Randver. Her father was angry that she had married without his permission. He was an old man, but he went to Gardariki with a large group of men.
One night, as they were harboured in the Gulf of Finland, he had a strange dream, and so he asked his foster-father Hörð. His foster-father was standing on a high cliff during the conversation and told Ivar that the dream foretold the death of Ivar and the end of his evil deeds. Ivar was so angry by these words that he threw himself down into the sea, whereupon also Hörð did the same thing.
As the throne of Sweden and Denmark was vacant, Auðr's son Harold Wartooth, departed to Scania to claim his inheritance, with the help of his stepfather Ráðbarðr.
According to Stories and Ballads of the Far Past- page 139, he married Asa, daughter of King Harold of the Red Mustache of Denmark.
Anglo-Saxon and Norse poems - Page 192
by Nora Kershaw Chadwick - Literary Criticism - 1922
A history of Sweden from the earliest times to the present day - Page 68
by Neander Nicolas Cronholm - History - 1902