Anderson–Kim's ergodicity conjecture for weakly reversible stochastic mass-action reaction systems

A stochastic mass-action reaction system (SMART) is a continuous-time Markov chain describing molecule counts in a mass-action reaction network, and it is weakly reversible when every reaction lies in a reaction pathway whose directed reaction graph returns to its source complex. Anderson–Kim's ergodicity conjecture. Every weakly reversible SMART is ergodic. This conjecture would generalize the known ergodicity theorem for complex-balanced SMARTs and concerns positive recurrence and long-term stochastic behavior of reaction networks. The source gives no resolution status.