Home | Contents | Submissions, editors, etc. | Login | Search | ECP
 Electronic Journal of Probability > Vol. 11 (2006) > Paper 16 open journal systems 


Fragmentation of ordered partitions and intervals

Anne-Laure Basdevant, Université Paris VI


Abstract
Fragmentation processes of exchangeable partitions have already been studied by several authors. This paper deals with fragmentations of exchangeable compositions, i.e. partitions of $mathbb{N}$ in which the order of the blocks matters. We will prove that such a fragmentation is bijectively associated to an interval fragmentation. Using this correspondence, we then study two examples : Ruelle's interval fragmentation and the interval fragmentation derived from the standard additive coalescent.


Full text: PDF

Pages: 394-417

Published on: May 29, 2006


Bibliography
  1. Aldous, David; Pitman, Jim. The standard additive coalescent. Ann. Probab. 26 (1998), no. 4, 1703--1726. MR1675063 (2000d:60121)
  2. Basdevant, Anne-Laure. Ruelle's probability cascades seen as a fragmentation process. Preprint math.PR/0501088, 2005. Math. Review number not available.
  3. Berestycki, Julien. Ranked fragmentations. ESAIM Probab. Statist. 6 (2002), 157--175 (electronic). MR1943145 (2004d:60196)
  4. Bertoin, Jean. A fragmentation process connected to Brownian motion. Probab. Theory Related Fields 117 (2000), no. 2, 289--301. MR1771665 (2002b:60136)
  5. Bertoin, Jean. Self-similar fragmentations. Ann. Inst. H. Poincaré Probab. Statist. 38 (2002), no. 3, 319--340. MR1899456 (2003h:60109)
  6. Bertoin, Jean. Random fragmentation and coagulation processes. Cambridge University Press, Cambridge, 2006. Math. Review number not available.
  7. Bertoin, Jean; Le Gall, Jean-François. The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes. Probab. Theory Related Fields 117 (2000), no. 2, 249--266. MR1771663 (2001h:60150)
  8. Bertoin, Jean; Pitman, Jim. Two coalescents derived from the ranges of stable subordinators. Electron. J. Probab. 5 (2000), no. 7, 17 pp. (electronic). MR1768841 (2002j:60082)
  9. Bolthausen, E.; Sznitman, A.-S. On Ruelle's probability cascades and an abstract cavity method. Comm. Math. Phys. 197 (1998), no. 2, 247--276. MR1652734 (99k:60244)
  10. Chassaing, Philippe; Janson, Svante. A Vervaat-like path transformation for the reflected Brownian bridge conditioned on its local time at 0. Ann. Probab. 29 (2001), no. 4, 1755--1779. MR1880241 (2003c:60137)
  11. Gnedin, Alexander V.. The representation of composition structures. Ann. Probab. 25 (1997), no. 3, 1437--1450. MR1457625 (98g:60019)
  12. Haas, Bénédicte; Miermont, Grégory. The genealogy of self-similar fragmentations with negative index as a continuum random tree. Electron. J. Probab. 9 (2004), no. 4, 57--97 (electronic). MR2041829 (2004m:60086)
  13. Kallenberg, Olav. Local hitting and conditioning in symmetric interval partitions. Stochastic Process. Appl. 94 (2001), no. 2, 241--270. MR1840832 (2002k:60091)
  14. Kerov, S. V. Asymptotic representation theory of the symmetric group and its applications in analysis. Translated from the Russian manuscript by N. V. Tsilevich. With a foreword by A. Vershik and comments by G. Olshanski. Translations of Mathematical Monographs, 219. American Mathematical Society, Providence, RI, 2003. xvi+201 pp. ISBN: 0-8218-3440-1 MR1984868 (2005b:20021)
  15. Kingman, J. F. C. The coalescent. Stochastic Process. Appl. 13 (1982), no. 3, 235--248. MR0671034 (84a:60079)
  16. Pitman, Jim. Exchangeable and partially exchangeable random partitions. Probab. Theory Related Fields 102 (1995), no. 2, 145--158. MR1337249 (96e:60059)
  17. Pitman, Jim. Coalescents with multiple collisions. Ann. Probab. 27 (1999), no. 4, 1870--1902. MR1742892 (2001h:60016)
  18. Pitman, Jim; Yor, Marc. The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25 (1997), no. 2, 855--900. MR1434129 (98f:60147)
  19. Ruelle, David. A mathematical reformulation of Derrida's REM and GREM. Comm. Math. Phys. 108 (1987), no. 2, 225--239. MR0875300 (88b:82016)
















Research
Support Tool
Capture Cite
View Metadata
Supplementary
Files and / or
CORRECTIONS
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | ECP

Electronic Journal of Probability. ISSN: 1083-6489