Here is an approach demonstrating an alternative to randomness, from Peikoff’s “Objectivism: The Philosophy of Ayn Rand”:

  The law of causality affirms a necessary connection between entities and their actions. It does not, however, specify any particular kind of entity or of action. The law does not say that only mechanistic relationships can occur, the kind that apply when one billiard ball strikes another; this is one common form of causation, but it does not preempt the field. Similarly, the law does not say that only choices governed by ideas and values are possible; this, too, is merely a form of causation; it is common but not universal within the realm of consciousness. The law of causality does not inventory the universe; it does not tell us what kinds of entities or actions are possible. It tells us only that whatever entities there are, they act in accordance with their nature, and whatever actions there are, they are performed and determined by the entity which acts.
  
  The law of causality by itself, therefore, does not affirm or deny the reality of an irreducible choice. It says only this much: if such a choice does exist, then it, too, as a form of action, is performed and necessitated by an entity of a specific nature.
  
  The content of one’s choice could always have gone in the opposite direction; the choice to focus could have been the choice not to focus, and vice versa. But the action itself, the fact of choosing as such, in one direction or the other, is unavoidable. Since man is an entity of a certain kind, since his brain and consciousness possess a certain identity, he must act in a certain way. He must continuously choose between focus and nonfocus. Given a certain kind of cause, in other words, a certain kind of effect must follow. This is not a violation of the law of causality, but an instance of it.

How is an unavoidable, if arbitrary, causality any different than determinism? That passage supports determinism, any never even argues for a free will, random or otherwise.