True-concurrency probabilistic models: Markov nets and a law of large numbers

We introduce the model of Markov nets, a probabilistic extension of safe Petri nets under the true-concurrency semantics—this means that traces, not firing sequences, are given a probability. This model builds upon our previous work on probabilistic event structures. We use the notion of a branching cell for event structures, and show that the latter provides an adequate conception of local state for nets. We prove a Law of Large Numbers (LLN) for Markov nets, which constitutes the main contribution of the paper. This LLN allows for the characterization, in a quantitative way, of the asymptotic behavior of Markov nets.