2024/01/09 by Andrea Collevecchio, Collevecchio, Andrea, Tuan-Minh Nguyen +1
Business, Management and Accounting · Mathematics · #60G17 #60G20 #60K35 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2401.04366
openalex publication_date 2024/01/09 · openalex created_date 2024/01/13 · openalex updated_date 2026/07/28
We study asymptotic behaviours of a non-linear vertex-reinforced jump process defined on an arbitrary infinite graph with bounded degree. We prove that if the reinforcement function w is reciprocally integrable and non-decreasing, then the process visits only a finite number of vertices. In the case where w is approximately equal to a super-linear polynomial, we show that the process eventually gets stuck on a star-shaped subgraph and there is exactly one vertex with unbounded local time.