A note on characterizing tightness of random sets of càdlàg paths. (English) Zbl 1453.82030
Birkner, Matthias (ed.) et al., Genealogies of interacting particle systems. Papers based on lectures and turorials of the National University of Singapore, Singapore, July 17 – Aug 18, 2017. Hackensack, NJ: World Scientific. Lect. Notes Ser., Inst. Math. Sci., Natl. Univ. Singap. 38, 295-313 (2020).
Summary: We record two natural tightness criteria for random sets of càdlàg paths, within the state space introduced by A. Etheridge et al. in [Electron. J. Probab. 22, Paper No. 39, 36 p. (2017; Zbl 1364.60104)]. This state space is the equivalent, for càdlàg paths, of the (continuous path) state space introduced for the Brownian web by L. R. G. Fontes et al. in [Ann. Probab. 32, No. 4, 2857–2883 (2004; Zbl 1105.60075)].
We discuss some implications of these criteria, in particular for cases of coalescing random walkers with heavy tailed jumps, in which tightness fails.
For the entire collection see [Zbl 1440.82004].
We discuss some implications of these criteria, in particular for cases of coalescing random walkers with heavy tailed jumps, in which tightness fails.
For the entire collection see [Zbl 1440.82004].
MSC:
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 60J65 | Brownian motion |
