Projects per year
Abstract
We study Random Walks in an i.i.d. Random Environment (RWRE) defined on bregular trees. We prove a functional central limit theorem (FCLT) for transient processes, under a moment condition on the environment. We emphasize that we make no uniform ellipticity assumptions. Our approach relies on regenerative levels, i.e. levels that are visited exactly once. On the way, we prove that the distance between consecutive regenerative levels have a geometrically decaying tail. In the second part of this paper, we apply our results to Linearly EdgeReinforced Random Walk (LERRW) to prove FCLT when the process is defined on bregular trees, with b≥4, substantially improving the results of the first author (see Theorem 3 of Collevecchio (2006)).
Original language  English 

Pages (fromto)  48924909 
Number of pages  18 
Journal  Stochastic Processes and their Applications 
Volume  130 
Issue number  8 
DOIs  
Publication status  Published  Aug 2020 
Keywords
 Functional central limit theorem
 Random walks in random environment
 Selfinteracting random walks
Projects
 2 Finished

Random walks with long memory
Collevecchio, A., Garoni, T., Hamza, K., Cotar, C. & Tarres, P.
Australian Research Council (ARC)
1/05/18 → 1/05/22
Project: Research

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. M., Taylor, P., Turner, I., Wand, M., Garoni, T., SmithMiles, 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 (QUT), University of Adelaide, University of New South Wales (UNSW), University of Queensland , University of Technology (UTS) 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