Is AlphaZero deterministic? AlphaZero searches for moves using Monte Carlo Tree Search (MCTS). As I understand MCTS, it takes the root position, goes to a child node, and then plays random moves until one side wins. Since the moves played are random, does that mean AlphaZero is also random?

Related: this question shows that Stockfish and other conventional engines are indeed deterministic if one looks only at the number of nodes evaluated. I don't know however if the same applies to AlphaZero.
No. MCTS is generally not deterministic. However, it's not that bad given how powerful Google's machines were.