Great explanation, I understand it better from a technical perspective.
I assume Troy is hidden to the authorities, who only have the Blockchain ledger and no other information to go on? That's waht I meant by "concentrated" above -- how likely is it that the Chinese government would find Troy and extract the information out of him with legal threats or with a heavy wrench?
I don't think the owner of the tumbler has any motivation to keep records (after each transaction is complete). So he deletes the records and spares himself the heavy wrench.
If Troy is trustworthy, he'll delete the transaction history.
However, there area number of attacks possible from Troy's perspective. He can keep a transaction history and use it to blackmail Alice and Bob. He can simply keep coins sent to the tumbler and send out nothing. It's very important that Troy be a trusted actor.
I assume Troy is hidden to the authorities, who only have the Blockchain ledger and no other information to go on? That's waht I meant by "concentrated" above -- how likely is it that the Chinese government would find Troy and extract the information out of him with legal threats or with a heavy wrench?