The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  1. Barbour, A. D.; Gnedin, A. V. Regenerative compositions in the case of slow variation. Stochastic Process. Appl. 116 (2006), no. 7, 1012--1047. MR2238612 (2007m:60133)
  2. Basdevant, A.-L. Ruelle's probability cascades seen as a fragmentation process. Markov Process. Related Fields 12 (2006), no. 3, 447--474. MR2246260 (2007h:60068)
  3. Berestycki, Julien; Berestycki, Nathanaël; Schweinsberg, Jason. Beta-coalescents and continuous stable random trees. Ann. Probab. 35 (2007), no. 5, 1835--1887. MR2349577
  4. Berestycki, Julien; Berestycki, Nathanaël; Schweinsberg, Jason. Small-time behavior of Beta-coalescents. arXiv:math/0601032. To appear in Ann. Inst. H. Poincaré Probab. Statist. (2007).
  5. 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)
  6. Birkner, Matthias; Blath, Jochen; Capaldo, Marcella; Etheridge, Alison; Möhle, Martin; Schweinsberg, Jason; Wakolbinger, Anton. Alpha-stable branching and beta-coalescents. Electron. J. Probab. 10 (2005), no. 9, 303--325 (electronic). MR2120246 (2006c:60100)
  7. 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)
  8. Chen, Hong; Yao, David D. Fundamentals of queueing networks. Performance, asymptotics, and optimization. Applications of Mathematics (New York), 46. Stochastic Modelling and Applied Probability. Springer-Verlag, New York, 2001. xviii+405 pp. ISBN: 0-387-95166-0 MR1835969 (2003c:60149)
  9. Darling, R. W. R.; Norris, J. R. Structure of large random hypergraphs. Ann. Appl. Probab. 15 (2005), no. 1A, 125--152. MR2115039 (2006a:05105)
  10. Darling, R. W. R.; Norris, J. R. Differential equation approximations for Markov chains. arXiv:0710.3269 (2007).
  11. Delmas, J.-F.; Dhersin, J.-S.; Siri-Jegousse, A. Asymptotic results on the length of coalescent trees. arXiv:0706.0204. To appear in Ann. Appl. Probab. (2007).
  12. Dong, Rui; Gnedin, Alexander; Pitman, Jim. Exchangeable partitions derived from Markovian coalescents. Ann. Appl. Probab. 17 (2007), no. 4, 1172--1201. MR2344303
  13. Drmota, Michael; Iksanov, Alex; Moehle, Martin; Roesler, Uwe. Asymptotic results concerning the total branch length of the Bolthausen-Sznitman coalescent. Stochastic Process. Appl. 117 (2007), no. 10, 1404--1421. MR2353033
  14. Durrett, Rick. Probability models for DNA sequence evolution. Probability and its Applications (New York). Springer-Verlag, New York, 2002. viii+240 pp. ISBN: 0-387-95435-X MR1903526 (2003b:60003)
  15. Ewens, W. J. The sampling theory of selectively neutral alleles. Theoret. Population Biology 3 (1972), 87--112; erratum, ibid. 3 (1972), 240; erratum, ibid. 3 (1972), 376. MR0325177 (48 #3526)
  16. Ewens, Warren J. Mathematical population genetics. I. Theoretical introduction. Second edition. Interdisciplinary Applied Mathematics, 27. Springer-Verlag, New York, 2004. xx+417 pp. ISBN: 0-387-20191-2 MR2026891 (2004k:92001)
  17. Gnedin, Alexander. Regenerative composition structures: characterisation and asymptotics of block counts. Joint work with Jim Pitman and Marc Yor. Trends Math., Mathematics and computer science. III, 441--443, Birkhäuser, Basel, 2004. MR2090532
  18. Gnedin, Alexander; Hansen, Ben; Pitman, Jim. Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws. Probab. Surv. 4 (2007), 146--171 (electronic). MR2318403
  19. Gnedin, Alexander; Pitman, Jim. Regenerative partition structures. Electron. J. Combin. 11 (2004), no. 2, Research Paper 12, 21 pp. (electronic). MR2120107 (2005k:60113)
  20. Gnedin, Alexander; Pitman, Jim; Yor, Marc. Asymptotic laws for compositions derived from transformed subordinators. Ann. Probab. 34 (2006), no. 2, 468--492. MR2223948 (2007c:60040)
  21. Gnedin, Alexander; Pitman, Jim; Yor, Marc. Asymptotic laws for regenerative compositions: gamma subordinators and the like. Probab. Theory Related Fields 135 (2006), no. 4, 576--602. MR2240701 (2007m:60018)
  22. Gnedin, Alexander; Yakubovich, Yuri. On the number of collisions in Lambda-coalescents. Electron. J. Probab. 12 (2007), no. 56, 1547--1567 (electronic). MR2365877
  23. Gnedin, Alexander V. The Bernoulli sieve. Bernoulli 10 (2004), no. 1, 79--96. MR2044594 (2004k:60018)
  24. Gnedin, Alexander V.; Yakubovich, Yuri. Recursive partition structures. Ann. Probab. 34 (2006), no. 6, 2203--2218. MR2294980 (2008a:60016)
  25. Goldschmidt, Christina; Martin, James B. Random recursive trees and the Bolthausen-Sznitman coalescent. Electron. J. Probab. 10 (2005), no. 21, 718--745 (electronic). MR2164028 (2006g:60112)
  26. Iksanov, A.; 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), 28--35 (electronic).
  27. Karlin, Samuel. Central limit theorems for certain infinite urn schemes. J. Math. Mech. 17 (1967) 373--401. MR0216548 (35 #7379)
  28. Kingman, J. F. C. Random partitions in population genetics. Proc. Roy. Soc. London Ser. A 361 (1978), no. 1704, 1--20. MR0526801 (58 #26167)
  29. Kingman, J. F. C. The representation of partition structures. J. London Math. Soc. (2) 18 (1978), no. 2, 374--380. MR0509954 (80a:05018)
  30. Kingman, J. F. C. The coalescent. Stochastic Process. Appl. 13 (1982), no. 3, 235--248. MR0671034 (84a:60079)
  31. Möhle, M. On sampling distributions for coalescent processes with simultaneous multiple collisions. Bernoulli 12 (2006), no. 1, 35--53. MR2202319
  32. Möhle, M. On the number of segregating sites for populations with large family sizes. Adv. in Appl. Probab. 38 (2006), no. 3, 750--767. MR2256876 (2008b:60164)
  33. Möhle, Martin. On a class of non-regenerative sampling distributions. Combin. Probab. Comput. 16 (2007), no. 3, 435--444. MR2312437 (2008c:60006)
  34. Pitman, Jim. Coalescents with multiple collisions. Ann. Probab. 27 (1999), no. 4, 1870--1902. MR1742892 (2001h:60016)
  35. Pitman, J. Combinatorial stochastic processes. Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, July 7--24, 2002. With a foreword by Jean Picard. Lecture Notes in Mathematics, 1875. Springer-Verlag, Berlin, 2006. x+256 pp. ISBN: 978-3-540-30990-1; 3-540-30990-X MR2245368 (2008c:60001)
  36. Pittel, Boris; Spencer, Joel; Wormald, Nicholas. Sudden emergence of a giant k-core in a random graph. J. Combin. Theory Ser. B 67 (1996), no. 1, 111--151. MR1385386 (97e:05176)
  37. Sagitov, Serik. The general coalescent with asynchronous mergers of ancestral lines. J. Appl. Probab. 36 (1999), no. 4, 1116--1125. MR1742154 (2001f:92019)
  38. Schweinsberg, Jason. A necessary and sufficient condition for the Lambda-coalescent to come down from infinity. Electron. Comm. Probab. 5 (2000), 1--11 (electronic). MR1736720 (2001g:60025)
  39. Whitt, Ward. Stochastic-process limits. An introduction to stochastic-process limits and their application to queues. Springer Series in Operations Research. Springer-Verlag, New York, 2002. xxiv+602 pp. ISBN: 0-387-95358-2 MR1876437 (2003f:60005)
  40. Wormald, Nicholas C. Differential equations for random processes and random graphs. Ann. Appl. Probab. 5 (1995), no. 4, 1217--1235. MR1384372 (97c:05139)

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.