What is a specific definition of the version of the American Dream in The Day of the Locust?
A specific definition of the American Dream in this novel would have to focus on the illusory nature of success and the way that this is presented through the description of the setting in Hollywood. Above all, Hollywood is described as a place that is dependent upon fantasies and dreams for its continued survival, and what is interesting is the way in which the novel draws a deliberate parallel between the movie sets that Tod designs and the one-dimensional and insubstantial life in Hollywood.
Therefore this novel presents the American Dream as being something that is fundamentally illusory and not real. However, what is key to understanding this novel is the way that it only continues to survive through the way in which so many characters suspend their disbelief to ensure its continued smooth running. Consider the kind of characters that are presented to us in this novel and the willing suspesion of disbelief that they engage in: we have Claude Estee who acts out the part of a Confederate general, even though his physical appearance clearly shows this is false, and then Harry Greener pretends he has had a great career as an actor, though the reality is that he was nothing more than a failure as a clown.
The definition of the American Dream therefore involves a certain amount of ambiguity. Not only does it exist as an illusion, but it is shown to exert immense power and influence over the characters, even though it is flimsy and insubstantial. It is the idea that lies behind the American Dream that is shown to be more real than that actual American Dream itself.