In what ways are Jay Gatsby in the Great Gatsby and Pearl in The Scarlet Letter similar?

Both Jay Gatsby and Pearl are estranged from their families. Jay Gatsby, or rather James Gatz, has chosen to live a completely different life from the one his family lives; although he paid for his parents' home, he does not maintain any significant contact with them because they would blow his cover. He pretends to be the heir to a family fortune so that he can pass himself off as "old money," and he's told people that his whole family is dead. Gatsby's distance from his family is both emotional and geographical. Pearl, on the other hand, lives near her parents, but she does not know—at least not consciously—who her father is. She is, of necessity, quite close to her mother, who is the only person she interacts with on a regular basis, but she remains at a considerable emotional remove from her father, a man who will not acknowledge her either privately (to Pearl, herself) or publicly.
In addition, both Gatsby and Pearl are rule breakers. Gatsby is a bootlegger, someone who illegally sells alcohol during Prohibition, making his fortune by engaging in a life of crime. He does it in order to make a lot of money quickly so that he can impress Daisy with his fortune and security. Pearl, as the narrator says, cannot "be made amenable to rules." She disobeys her mother constantly; her behavior often flies in the face of social convention, and she will not listen, even when prevailed upon by the minister, governor, or the like. Gatsby and Pearl both live, to varying degrees, outside the rules of their communities.
Finally, Gatsby and Pearl are also mysteries to their communities. His party guests speculate wildly about Gatsby's origins, history, and occupation; no one really knows him, let alone knows him well, and this likely helps him to cultivate the fascinating facade he wants to create. Pearl is also an unknown quantity among her community. She doesn't speak to many people besides her mother, and she slings mud and rocks at other children whenever they come near. Both Gatsby and Pearl are alienated from and considered to be mysterious by their societies.