Download this PDF file Fullscreen Fullscreen Off
References
- Berestycki, Julien; Berestycki, Nathanaël; Schweinsberg, Jason. Beta-coalescents and continuous stable random trees. Ann. Probab. 35 (2007), no. 5, 1835--1887. MR2349577
- Berestycki, Julien; Berestycki, Nathanaël; Schweinsberg, Jason. Small-time behavior of beta coalescents. Ann. Inst. Henri Poincaré Probab. Stat. 44 (2008), no. 2, 214--238. MR2446321
- Bertoin, Jean; Le Gall, Jean-Francois. Stochastic flows associated to coalescent processes. III. Limit theorems. Illinois J. Math. 50 (2006), no. 1-4, 147--181 (electronic). MR2247827
- 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
- Dahmer, I., Kersting, G., and Wakolbinger, A.: The total external branch length of beta coalescents. arXiv:1212.6070, to appear in Comb. Probab. Comput.
- Delmas, Jean-François; Dhersin, Jean-Stéphane; Siri-Jegousse, Arno. Asymptotic results on the length of coalescent trees. Ann. Appl. Probab. 18 (2008), no. 3, 997--1025. MR2418236
- Gnedin, Alexander; Yakubovich, Yuri. On the number of collisions in Lambda-coalescents. Electron. J. Probab. 12 (2007), no. 56, 1547--1567. MR2365877
- Greven, Andreas; Pfaffelhuber, Peter; Winter, Anita. Tree-valued resampling dynamics martingale problems and applications. Probab. Theory Related Fields 155 (2013), no. 3-4, 789--838. MR3034793
- Kersting, Götz. The asymptotic distribution of the length of beta-coalescent trees. Ann. Appl. Probab. 22 (2012), no. 5, 2086--2107. MR3025690
- Kingman, J. F. C. The coalescent. Stochastic Process. Appl. 13 (1982), no. 3, 235--248. MR0671034
- Iksanov, Alex; Möhle, Martin. On the number of jumps of random walks with a barrier. Adv. in Appl. Probab. 40 (2008), no. 1, 206--228. MR2411821
- Pfaffelhuber, P.; Wakolbinger, A. The process of most recent common ancestors in an evolving coalescent. Stochastic Process. Appl. 116 (2006), no. 12, 1836--1859. MR2307061
- Pfaffelhuber, P.; Wakolbinger, A.; Weisshaupt, H. The tree length of an evolving coalescent. Probab. Theory Related Fields 151 (2011), no. 3-4, 529--557. MR2851692
- Pitman, Jim. Coalescents with multiple collisions. Ann. Probab. 27 (1999), no. 4, 1870--1902. MR1742892
- Sagitov, Serik. The general coalescent with asynchronous mergers of ancestral lines. J. Appl. Probab. 36 (1999), no. 4, 1116--1125. MR1742154
- Samorodnitsky, Gennady; Taqqu, Murad S. Stable non-Gaussian random processes. Stochastic models with infinite variance. Stochastic Modeling. Chapman & Hall, New York, 1994. xxii+632 pp. ISBN: 0-412-05171-0 MR1280932
- Schweinsberg, Jason. Coalescent processes obtained from supercritical Galton-Watson processes. Stochastic Process. Appl. 106 (2003), no. 1, 107--139. MR1983046
- Schweinsberg, Jason. Dynamics of the evolving Bolthausen-Sznitman coalecent. [Dynamics of the evolving Bolthausen-Sznitman coalescent] Electron. J. Probab. 17 (2012), no. 91, 50 pp. MR2988406
- Siri-Jégousse, A. and Yuan, L. Asymptotics of the minimal clade size and related functionals of certain beta-coalescents. arXiv:1311.5819.
- Steinrücken, M., Birkner, M., and Blath, J.: Analysis of DNA sequence variation within marine species using Beta-coalescents. Theor. Pop. Biol. 87 (2013), 15--24.
This work is licensed under a Creative Commons Attribution 3.0 License.