2023/05/12 by Disertori, Margherita, Merkl, Franz, Rolles, Silke W. W. · 1 citation
#60K37 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 60K35 #Probability (math.PR) #secondary 60G60
paper · doi:10.48550/arxiv.2305.07359
We show that the vertex-reinforced jump process on the d-dimensional lattice with long-range jumps is transient in any dimension d as long as the initial weights do not decay too fast. The main ingredients in the proof are: an analysis of the corresponding random environment on finite boxes, a comparison with a hierarchical model, and the reduction of the hierarchical model to a non-homogeneous effective one-dimensional model. For d≥ 3 we also prove transience of the vertex-reinforced jump process with possibly long-range jumps as long as nearest-neighbor weights are large enough.