Asymptotic results concerning the total branch length of the Bolthausen-Sznitman coalescent

Stochastic Processes and their Applications

Volumn 117, Issue 10, 2007, Pages 1404-1421

  Drmota, Michael ^a   Iksanov, Alex ^b   Moehle, Martin ^c   Roesler, Uwe ^d  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV   (Ukraine)

^c UNIVERSITY OF TÜBINGEN   (Germany)

^d UNIVERSITY OF KIEL   (Germany)

Author keywords

Asymptotic expansion; Bolthausen Sznitman coalescent; Generating functions; Random recursive trees; Stable limit

Indexed keywords

PROBABILITY DISTRIBUTIONS; RANDOM VARIABLES; RECURSIVE FUNCTIONS; TREES (MATHEMATICS);

ASYMPTOTIC EXPANSION; BOLTHAUSEN SZNITMAN COALESCENT; GENERATING FUNCTIONS; RANDOM RECURSIVE TREES;

ASYMPTOTIC ANALYSIS;

EID: 33847619112     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2007.01.011     Document Type: Article

References (26)

1. J. Berestycki, N. Berestycki, J. Schweinsberg, 2007. Small-time behavior of beta coalescents. Ann. Inst. H. Poincare Probab. Statist. (in press)
2. Bertoin J., and Le Gall J.-F. The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes. Probab. Theory Related Fields 117 (2000) 249-266
3. Bertoin J., and Pitman J. Two coalescents derived from the ranges of stable subordinators. Electron. J. Probab. 5 (2000) 1-17
4. Bingham N.H., Goldie C.M., and Teugels J.L. Regular Variation (1987), Cambridge University Press
5. Bolthausen E., and Sznitman A.-S. On Ruelle's probability cascades and an abstract cavity method. Comm. Math. Phys. 197 (1998) 247-276
6. Bovier A., and Kurkova I. Much ado about Derrida's GREM. In: Bolthausen E., and Bovier A. (Eds). Spin Glasses. Lecture Notes in Mathematics vol. 1900 (2006), Springer, Berlin
7. M. Drmota, A. Iksanov, M. Moehle, U. Roesler, A limiting distribution for the number of cuts needed to isolate the root of a random recursive tree, 2006. Preprint
8. J.A. Fill, N. Kapur, A. Panholzer, Destruction of very simple trees, Algorithmica (2006-2007) (in press)
9. Goldschmidt C., and Martin J.B. Random recursive trees and the Bolthausen-Sznitman coalescent. Electron. J. Probab. 10 (2005) 718-745
10. Iksanov A., and Möhle M. A probabilistic proof of a weak limit law for the number of cuts needed to isolate the root of a random recursive tree. Electron. Comm. Probab. 12 (2007) 36-43
11. Janson S. Random records and cuttings in complete binary trees. Mathematics and Computer Science vol. III (2004), Birkhäuser, Basel 241-253
12. Janson S. Random cutting and records in deterministic and random trees. Random Structures Algorithms 29 (2006) 139-179
13. Kingman J.F.C. The coalescent. Stochastic Process. Appl. 13 (1982) 235-248
14. Kingman J.F.C. Origins of the coalescent. Genetics 156 (2000) 1461-1463
15. Meir A., and Moon J.W. Cutting down recursive trees. Math. Biosci. 21 (1974) 173-181
16. Möhle M. Convergence results for compound Poisson distributions and applications to the standard Luria-Delbrück distribution. J. Appl. Probab. 42 (2005) 620-631
17. Möhle M. On the number of segregating sites for populations with large family sizes. Adv. Appl. Probab. 38 (2006) 750-767
18. Neininger R., and Rüschendorf L. On the contraction method with degenerate limit equation. Ann. Probab. 32 (2004) 2838-2856
19. Panholzer A. Destruction of recursive trees. Mathematics and Computer Science vol. III (2004), Birkhäuser, Basel 267-280
20. Panholzer A. Cutting down very simple trees. Questions Math. 29 (2006) 211-227
21. Pitman J. Coalescents with multiple collisions. Ann. Probab. 27 (1999) 1870-1902
22. Sagitov S. The general coalescent with asynchronous mergers of ancestral lines. J. Appl. Probab. 36 (1999) 1116-1125
23. Tavaré S. Line of descent and genealogical processes, and their applications in population genetics models. Theor. Pop. Biol. 26 (1984) 119-164
24. Tavaré S. Ancestral inference in population genetics. Lectures on Probability and Statistics 1-188. Lecture Notes in Mathematics vol. 1837 (2004), Springer, Berlin
25. J. Wakeley, Coalescent Theory: An Introduction, Roberts and Company Publishers, Greenwood Village, ISBN: 0-9747077-5-9, 2007 (in press)
26. Wiuf C., and Hein J. Recombination as a point process along sequences. Theor. Pop. Biol. 55 (1999) 248-259