The spatial Λ-coalescent

Electronic Journal of Probability

Volumn 11, Issue , 2006, Pages 363-393

  Limic, Vlada ^a   Sturm, Anja ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF DELAWARE   (United States)

Author keywords

Coalescent; Coalescing random walks; Limit theorems; Structured coalescent; coalescent

Indexed keywords

EID: 33646790878     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v11-319     Document Type: Article

References (28)

1. Aldous, D.J. (1999) Deterministic and stochastic models for coalescence (aggregation, coagulation): A review of the mean-field theory for Probabilists. Bernoulli 5, 3-48.
2. Arratia, R. (1979) Coalescing Brownian motion and the whole voter model on Z. Ph.D. disertation. Univ. Wisconsin-Madison.
3. Barton, N.H., Etheridge, A.M., and Sturm, A.K. (2004) Coalescence in a random background, Ann. Appl. Probab. 14 (2), 754-785.
4. Bramson, M. and Griffeath, D. (1980) Asymptotics for interacting particle systems on Zd, Z. Wahrscheinlichkeit verw. Gebiete, 53, 183-196.
5. Berestycki, J. (2004) Exchangeable fragmentation-coalescence processes and their equilibrium measures, Electronic J. Probab. 9, 770-824.
6. Berestycki, J., Berestycki, N., and Schweinsberg, J. (2005) Continuous-state branching processes and the properties of beta coalescents. Preprint.
7. Bertoin, J. and Le Gall, J.-F. (2000) The Bolthausen-Sznitman coalescent and the genealogy of continuous-state branching processes, Probab. Theory Relat. Fields, 117, 249-266.
8. Bertoin, J. and Le Gall, J.-F. (2003) Stochastic flows associated to coalescent processes. Probab. Theory Relat. Fields, 126, 261-288.
9. Bertoin, J. and Le Gall, J.-F. (2005) Stochastic flows associated to coalescent processes III: Limit theorems. preprint at arXiv.org: math.PR/0506092
10. Birkner, M., Blath, J., Capaldo, M., Etheridge, A., Mohle, M., Schweinsberg, J., Wakolbinger, A. (2005) Alpha-stable branching and Beta coalescents, Electronic J. Probab, 10 (9), 303-325.
11. Bolthausen, E. and Sznitman, A (1998) On Ruelle's probability cascades and an abstract cavity method, Comm. Math. Phys. 197, 247-276.
12. Cox, J.T. (1989) Coalescing random walks and voter model consensus times on the torus in Zd, Ann. Probab., 17, 1333-1366.
13. Durrett, R and Schweinsberg, J. (2005) A coalescent model for the effect of advantageous mutations on the genealogy of a population. Stochastic Process. Appl., 115 1628-1657.
14. Ethier, S. N. and Kurtz, T. G. (1986), Markov processes: characterization and convergence, Wiley Series in Probability and Mathematical Statistics.
15. Evans, S. N. and Pitman, J. (1998) Construction of Markovian coalescents, Ann. Inst. Henri Poincare, 34 (3), 339-383.
16. Greven, A., Limic, V., and Winter, A. (2005) Representation theorems for interacting Moran models, interacting Fisher-Wright diffusions and applications, Electronic J. Probab., 10 (39), 1286-1358.
17. Greven, A., Limic, V., and Winter, A. (2006) Coalescent processes arising in a study of diffusive clustering in preparation.
18. Greven, A., Limic, V., and Winter, A. (2006) Large Cluster formation in spatial Moran models in critical dimension via particle representations, in preparation.
19. Herbots, H. M. (1997) The structured coalescent, in P. Donnelly and S. Tavare, editors, Progress of Population Genetics and Human Evolution, pages 231-255, Springer.
20. Kingman, J.F.C. (1982) The coalescent, Stochastic Process. Appl., 13, 235-248.
21. Möhle, M. and Sagitov, S. (2001) A Classification of coalescent processes for haploid exchangeable population models, Ann. Probab. 29, 1547-1562.
22. Notohara, M. (1990) The coalescent and the genealogical process in geographically structured populations, Journal of Mathematical Biology, 31, 841-852.
23. Pitman, J. (1999) Coalescents with multiple collisions, Ann. Probab. 27 (4), 1870-1902.
24. Rogers, L.C.G. and Williams, D. (1979) Diffusion, Markov Processes and Martingales, Volume I Cambridge University Press.
25. Sagitov, S. (1999) The general coalescent with asynchronous mergers of ancestral lines, J. Appl. Prob. 36 (4), 1116-1125.
26. Schweinsberg, J. (2000) A necessary and sufficient condition for the A-coalescent to come down from infinity, Electr. Comm. Probab. 5, 1-11.
27. Schweinsberg, J. (2003) Coalescent processes obtained from supercritical Galton-Watson processes. Stochastic Process. Appl., 106, 107-139.
28. Zöhle, I., Cox, J.T., and Durrett, R. (2005) The stepping stone model. II: Genealogies and the infinite sites model. Ann. Appl. Probab., 15 (1B), 671-699.