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

References

  • Athreya, Krishna B.; Ghosh, Arka P.; Sethuraman, Sunder. Growth of preferential attachment random graphs via continuous-time branching processes. Proc. Indian Acad. Sci. Math. Sci. 118 (2008), no. 3, 473--494. MR2450248
  • Barabási, Albert-László; Albert, Réka. Emergence of scaling in random networks. Science 286 (1999), no. 5439, 509--512. MR2091634
  • Bollobás, B. and Riordan, O.: Mathematical results on scale-free graphs. phHandbook of Graphs and Networks (S. Bornholdt and H. Schuster, eds.), Wiley-VCH, Berlin, (2002).
  • Bollobás, Béla; Riordan, Oliver; Spencer, Joel; Tusnády, Gábor. The degree sequence of a scale-free random graph process. Random Structures Algorithms 18 (2001), no. 3, 279--290. MR1824277
  • Cooper, Colin. Distribution of vertex degree in web-graphs. Combin. Probab. Comput. 15 (2006), no. 5, 637--661. MR2248318
  • Cooper, Colin; Frieze, Alan. A general model of web graphs. Random Structures Algorithms 22 (2003), no. 3, 311--335. MR1966545
  • Darling, R. W. R.; Norris, J. R. Differential equation approximations for Markov chains. Probab. Surv. 5 (2008), 37--79. MR2395153
  • Deijfen, Maria; van den Esker, Henri; van der Hofstad, Remco; Hooghiemstra, Gerard. A preferential attachment model with random initial degrees. Ark. Mat. 47 (2009), no. 1, 41--72. MR2480915
  • Dereich, Steffen; Mörters, Peter. Random networks with sublinear preferential attachment: degree evolutions. Electron. J. Probab. 14 (2009), no. 43, 1222--1267. MR2511283
  • Ethier, Stewart N.; Kurtz, Thomas G. Markov processes. Characterization and convergence. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. x+534 pp. ISBN: 0-471-08186-8 MR0838085
  • Janson, Svante. Asymptotic degree distribution in random recursive trees. Random Structures Algorithms 26 (2005), no. 1-2, 69--83. MR2116576
  • Lu, Jiang; Feng, Qilin. Strong consistency of the number of vertices of given degrees in nonuniform random recursive trees. Yokohama Math. J. 45 (1998), no. 1, 61--69. MR1617833
  • Luczak, Malwina J. A quantitative law of large numbers via exponential martingales. Stochastic inequalities and applications, 93--111, Progr. Probab., 56, Birkhäuser, Basel, 2003. MR2073429
  • Luczak, Malwina J.; McDiarmid, Colin. On the maximum queue length in the supermarket model. Ann. Probab. 34 (2006), no. 2, 493--527. MR2223949
  • Luczak, Malwina J.; Norris, James. Strong approximation for the supermarket model. Ann. Appl. Probab. 15 (2005), no. 3, 2038--2061. MR2152252
  • Smythe, Robert T.; Mahmoud, Hosam M. A survey of recursive trees. (Ukrainian) ; translated from Teor. Ĭmovīr. Mat. Stat. No. 51 (1994), 1--29 Theory Probab. Math. Statist. No. 51, (1995), 1--27 (1996) MR1445048
  • Mahmoud, Hosam M.; Smythe, R. T.; Szymański, Jerzy. On the structure of random plane-oriented recursive trees and their branches. Random Structures Algorithms 4 (1993), no. 2, 151--176. MR1206674
  • McDiarmid, Colin. Concentration. Probabilistic methods for algorithmic discrete mathematics, 195--248, Algorithms Combin., 16, Springer, Berlin, 1998. MR1678578
  • Móri, Tamás F. The maximum degree of the Barabási-Albert random tree. Combin. Probab. Comput. 14 (2005), no. 3, 339--348. MR2138118
  • Norris, J. R. Markov chains. Reprint of 1997 original. Cambridge Series in Statistical and Probabilistic Mathematics, 2. Cambridge University Press, Cambridge, 1998. xvi+237 pp. ISBN: 0-521-48181-3 MR1600720
  • Rudas, Anna; Tóth, Bálint; Valkó, Benedek. Random trees and general branching processes. Random Structures Algorithms 31 (2007), no. 2, 186--202. MR2343718
  • Szymański, Jerzy. On a nonuniform random recursive tree. Random graphs '85 (Poznań, 1985), 297--306, North-Holland Math. Stud., 144, North-Holland, Amsterdam, 1987. MR0930497
  • Szymański, Jerzy. Concentration of vertex degrees in a scale-free random graph process. Random Structures Algorithms 26 (2005), no. 1-2, 224--236. MR2116583
  • Talagrand, Michel. Concentration of measure and isoperimetric inequalities in product spaces. Inst. Hautes Études Sci. Publ. Math. No. 81 (1995), 73--205. MR1361756
  • Yule, G.: A mathematical theory of evolution based on the conclusions of Dr. J. C. Willis Phil. Trans. Roy. Soc. London B213, (1925), 21--87.


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