Research output per year
Research output per year
Andrea Collevecchio, Tuan Minh Nguyen, Stanislav Volkov
Research output: Contribution to journal › Article › Research › peer-review
We consider a nonlinear vertex-reinforced jump process (VRJP(w)) on Z with an increasing measurable weight function w : [1, ∞) → [1, ∞) and initial weights equal to one. Our main goal is to study the asymptotic behaviour of VRJP(w) depending on the integrability of the reciprocal of w. In particular, we prove that if (Equation presented). then the process is recurrent, that is, it visits each vertex infinitely often and all local times are unbounded. On the other hand, if (Equation presented). and there exists a ρ > 0 such that (Equation presented). du is nonincreasing then the process will eventually get stuck on exactly three w(u) vertices, and there is only one vertex with unbounded local time. We also show that if the initial weights are all the same, VRJP on Z cannot be transient, that is, there exists at least one vertex that is visited infinitely often. Our results extend the ones previously obtained by Davis and Volkov (Probab. Theory Related Fields 123 (2002) 281-300) who showed that VRJP with linear reinforcement on ℤ is recurrent.
Original language | English |
---|---|
Pages (from-to) | 2671-2705 |
Number of pages | 35 |
Journal | Annals of Applied Probability |
Volume | 32 |
Issue number | 4 |
DOIs | |
Publication status | Published - Aug 2022 |
Research output: Other contribution › Research
Collevecchio, A., Garoni, T., Hamza, K., Cotar, C. & Tarres, P.
Australian Research Council (ARC)
1/05/18 → 1/05/22
Project: Research
Hall, P., Bartlett, P., Bean, N., Burrage, K., DeGier, J., Delaigle, A., Forrester, P., Geweke, J., Kohn, R., Kroese, D., Mengersen, K. L., Pettit, A., Pollett, P., Roughan, M., Ryan, L. M., Taylor, P., Turner, I., Wand, M., Garoni, T., Smith-Miles, K. A., Caley, M., Churches, T., Elazar, D., Gupta, A., Harch, B., Tam, S., Weegberg, K., Willinger, W. & Hyndman, R.
Australian Research Council (ARC), Monash University – Internal Department Contribution, University of Melbourne, Queensland University of Technology , University of Adelaide, University of New South Wales (UNSW), University of Queensland , University of Technology Sydney, Monash University – Internal University Contribution, Monash University – Internal Faculty Contribution, Monash University – Internal School Contribution, Roads Corporation (trading as VicRoads) (Victoria)
1/01/17 → 31/12/21
Project: Research