Free Access
Volume 25, 2021
Page(s) 204 - 219
Published online 23 March 2021
  1. G.K. Alexopoulos, Random walks on discrete groups of polynomial volume growth. Ann. Probab. 30 (2002) 723–801. [Google Scholar]
  2. O.S.M. Alves, F.P. Machado and S.Y. Popov, The shape theorem for the frog model. Ann. Appl. Probab. 12 (2002) 533–546. [Google Scholar]
  3. A. Auffinger, M. Damron and J. Hanson, 50 years of first-passage percolation. Vol. 68 of University Lecture Series. American Mathematical Society, Providence, RI (2017). [CrossRef] [Google Scholar]
  4. T. Austin, Integrable measure equivalence for groups of polynomial growth. Groups Geom. Dyn. 10 (2016) 117–154. [Google Scholar]
  5. H. Bass, The degree of polynomial growth of finitely generated nilpotent groups. Proc. London Math. Soc. 25 (1972) 603–614. [Google Scholar]
  6. E. Beckman, E. Dinan, R. Durrett, R. Huo and M. Junge, Asymptotic behavior of the Brownian frog model. Electr. J. Probab. 23 (2018) 19 pp. [Google Scholar]
  7. I. Benjamini and R. Tessera, First passage percolation on nilpotent Cayley graphs. Electr. J. Probab. 20 (2015) 20 pp. [Google Scholar]
  8. E. Breuillard, Geometry of locally compact groups of polynomialgrowth and shape of large balls. Groups Geom. Dyn. 8 (2014) 669–732. [CrossRef] [Google Scholar]
  9. R. Burioni and D. Cassi, Random walks on graphs: ideas, techniques and results. J. Phys. A. 38 (2005) R45. [CrossRef] [Google Scholar]
  10. M. Cantrell and A. Furman, Asymptotic shapes for ergodic families of metrics on nilpotent groups. Groups Geom. Dyn. 11 (2017) 1307–1345. [CrossRef] [Google Scholar]
  11. D.H. Fuk and S.V. Nagaev, Probabilistic inequalities for sums of independent random variables. Teor. Verojatnost. i Primenen. 16 (1971) 660–675. [Google Scholar]
  12. M. Gromov, Groups of polynomial growth and expanding maps. Publ. Math. IHES 53 (1981) 53–78. [CrossRef] [Google Scholar]
  13. C. Hoffman, T. Johnson and M. Junge, Recurrence and transience for the frog model on trees. Ann. Probab. 45 (2017) 2826–2854. [Google Scholar]
  14. C. Hoffman, T. Johnson and M. Junge, Infection spread for the frog model on trees. Electr. J. Probab. 24 (2019) 112. [Google Scholar]
  15. E. Kosygina and M.P.W. Zerner, A zero-one law for recurrence and transience of frog processes. Probab. Theory Related Fields 168 (2017) 317–346. [Google Scholar]
  16. E. Lebensztayn, F.P. Machado and S. Popov, An improved upper bound for the critical probability of the frog model on homogeneous trees. J. Stat. Phys. 119 (2005) 331–345. [Google Scholar]
  17. E. Lebensztayn and P.M. Rodriguez, A connection between a system of random walks and rumor transmission. Phys. A 392 (2013) 5793–5800. [Google Scholar]
  18. P. Pansu, Croissance des boules et des géodésiques fermées dans les nilvariétés. Ergodic Theory Dyn. Syst. 3 (1983) 415–445. [Google Scholar]
  19. A.F. Ramírez and V. Sidoravicius, Asymptotic behavior of a stochastic combustion growth process. J. Eur. Math. Soc. (JEMS) 6 (2004) 293–334. [Google Scholar]
  20. A. Telcs and N.C. Wormald, Branching and tree indexed random walks on fractals. J. Appl. Probab. 36 (1999) 999–1011. [Google Scholar]
  21. W. Woess, Random walks on infinite graphs and groups. Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, UK (2000). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.