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a markov chain is a very specific and different thing
LLM inference fits the definition a Markov chain, where the state is the input string to the LLM and the LLM's output is taken to be the probability distribution for the next state transition. The state space is the finite set of token strings fitting in the LLM's context window. The process of selecting the next token to output thus follows the Markov property. A whole readable string of text is generated by iterating this Markov process until the current state ends in an end-of-string token (or some other method).
As an aside, this is one major reason why people say thay LLMs can't learn. They are memoryless. Their output is wholly derived from the input state in a deterministic manner (barring inconsistencies in hardware or execution environment) that does not change after training (which is a separate process from inference).
ok but basically anything is markovian if you include enough in the state, which doesn't feel like it fits with what op was trying to imply
also I'd argue sampling makes it non deterministic