Unique-games invariant-measure transition conjecture

Consider the dynamical systems constructed from instances of the unique games conjecture, with alphabet size $k$, and let the invariant measure assign weight to neighborhoods of optimal or feasible assignments. Unique-games invariant-measure transition conjecture. As the alphabet size $k$ increases, the weight of the invariant measure in the vicinity of an optimal or feasible assignment transitions from subexponential to exponential scaling. The proposed transition is motivated by the paper's numerical observations, which are described as consistent with the unique games conjecture; theoretical bounds on the decay rates remain future work.