A spectral decomposition for the block counting process of the bolthausen-sznitman coalescent

Electronic Communications in Probability

Volumn 19, Issue , 2014, Pages

  Möhle, Martin ^a   Pitters, Helmut ^b  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Absorption time; Bolthausen sznitman coalescent; Green matrix; Hitting probabilities; Spectral decomposition; Stirling numbers

Indexed keywords

EID: 84905044198     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: 10.1214/ECP.v19-3464     Document Type: Article

References (16)

1. Abramowitz, M. and Stegun, I. A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. 9th printing. Dover, New York, 1972. MR-0757537
2. Bolthausen, E. and Sznitman, A.-S.: On Ruelle's probability cascades and an abstract cavity method. Commun. Math. Phys. 197, (1998), 247-276. MR-1652734
3. Drmota, M., Iksanov, A., Möhle, M. and Rösler, U.: Asymptotic results concerning the total branch length of the Bolthausen-Sznitman coalescent. Stoch. Process. Appl. 117, (2007), 1404-1421. MR-2353033
4. Freund, F. and Möhle, M.: On the time back to the most recent common ancestor and the external branch length of the Bolthausen-Sznitman coalescent. Markov Process. Related Fields 15, (2009), 387-416. MR-2554368
5. Gladstien, K.: The characteristic values and vectors for a class of stochastic matrices arising in genetics. SIAM J. Appl. Math. 34, (1978), 630-642. MR-0475977
6. Goldschmidt, C. and Martin, J. B.: Random recursive trees and the Bolthausen-Sznitman coalescent. Electron. J. Probab. 10, (2005), 718-745. MR-2164028
7. Henard, O.: The fixation line. Preprint, (2013). arXiv:1307.0784
8. Kingman, J.F.C.: On the genealogy of large populations. J. Appl. Probab. 19, (1982), 27-43. MR-0633178
9. Kukla, J., Miller, L. and Pitters, H.: A spectral decomposition for the Kingman and the Bolthausen-Sznitman coalescent. In preparation, (2014+).
10. Möhle, M.: On hitting probabilities of beta coalescents and absorption times of coalescents that come down from infinity. ALEA Lat. Am. J. Probab. Math. Stat. 11, (2014), 141-159.
11. Möhle, M.: Asymptotic hitting probabilities for the Bolthausen-Sznitman coalescent. J. Appl. Probab. 51A, (2014), to appear.
12. Möhle, M. and Pitters, H.: Absorption time and tree length of the Kingman coalescent and the Gumbel distribution. Preprint, (2014).
13. Norris, J. R.: Markov Chains. Cambridge University Press, Cambridge, 1997. MR-1600720
14. Pitman, J.: Coalescents with multiple collisions. Ann. Probab. 27, (1999), 1870-1902. MR-1742892
15. Sagitov, S.: The general coalescent with asynchronous mergers of ancestral lines. J. Appl. Probab. 36, (1999), 1116-1125. MR-1742154
16. Tavare, S.: Line-of-descent and genealogical processes, and their applications in population genetics models. Theor. Popul. Biol. 26, (1984), 119-164. MR-0770050