Phase diagram for once-reinforced random walks on trees with exponential weighting scheme
The reinforced random walk on a graph is defined by a weighting scheme that depends on the current local times of the walker and prefers steps to locations previously visited. The once-edge-reinforced random walk gives initial weight one to any edge and increases it by some fixed amount as soon as the edge has been crossed at least once; afterwards the weight remainsu unchanged. In this model, the absence of a recurrence-transience phase transition is known. The authors introduce a variant of a once-reinforced random walk on trees, which admits such a transition. For trees of bounded degree and supercritical Galton-Watson trees, they can give the whole picture of the phase diagram.
scientific article; zbMATH DE number 5372840
scientific article