Projects per year
We give a simple proof for recurrence of vertex reinforced jump process on Zd, under strong reinforcement. Moreover, we show how the previous result implies that linearly edge-reinforced random walk on Zd is recurrent for strong reinforcement. Finally, we prove that the H(2|2) model on Zd localizes at strong disorder. Even though these results are well-known, we propose a unified approach, which also has the advantage to provide shorter proofs, and relies on estimating fractional moments, introduced by Aizenman and Molchanov.
- Vertex-reinforced jump process
ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights
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., 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, 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