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References

  • Barabasi, Albert-Laszlo; Albert, Reka. Emergence of scaling in random networks. Science 286 (1999), no. 5439, 509--512. MR2091634
  • Benaim, Michel. Dynamics of stochastic approximation algorithms. Seminaire de Probabilites, XXXIII, 1--68, Lecture Notes in Math., 1709, Springer, Berlin, 1999. MR1767993
  • Chen, May-Ru; Wei, Ching-Zong. A new urn model. J. Appl. Probab. 42 (2005), no. 4, 964--976. MR2203815
  • Dereich, Steffen; Morters, Peter. Random networks with sublinear preferential attachment: degree evolutions. Electron. J. Probab. 14 (2009), no. 43, 1222--1267. MR2511283
  • Dommers, Sander; van der Hofstad, Remco; Hooghiemstra, Gerard. Diameters in preferential attachment models. J. Stat. Phys. 139 (2010), no. 1, 72--107. MR2602984
  • D'Souza, R. M.; Krapivsky, P. L.; Moore, C. The power of choice in growing trees. Eur. Phys. J. B 59 (2007), no. 4, 535--543. MR2358054
  • Flaxman, Abraham; Frieze, Alan; Fenner, Trevor. High degree vertices and eigenvalues in the preferential attachment graph. Internet Math. 2 (2005), no. 1, 1--19. MR2166274
  • Galashin, P. A., phExistence of a persistent hub in the convex preferential attachment model, arXiv:1310.7513.
  • Krapivsky, P. L. and Redner, S., phChoice-Driven Phase Transition in Complex Networks, arXiv:1312.7803.
  • Krapivsky, P. L., Redner, S., and Leyvraz, F. phConnectivity of growing random networks, Phys. Rev. Lett. 85 (2000), 4629--4632, URL: doi:10.1103/PhysRevLett.85.4629.
  • Kuba, Markus; Mahmoud, Hosam; Panholzer, Alois. Analysis of a generalized Friedman's urn with multiple drawings. Discrete Appl. Math. 161 (2013), no. 18, 2968--2984. MR3126664
  • Kushner, Harold J.; Clark, Dean S. Stochastic approximation methods for constrained and unconstrained systems. Applied Mathematical Sciences, 26. Springer-Verlag, New York-Berlin, 1978. x+261 pp. ISBN: 0-387-90341-0 MR0499560
  • Malyshkin, Y. and Paquette, E., phThe power of 2 choices over preferential attachment, arXiv:1311.1091.
  • bysame, phThe power of choice combined with preferential attachment, arXiv:1403.4301v1.
  • Mori, Tamas F. The maximum degree of the Barabasi-Albert random tree. Combin. Probab. Comput. 14 (2005), no. 3, 339--348. MR2138118
  • Peköz, E. A., Ross, N., and Röllin, A., phJoint degree distributions of preferential attachment random graphs, arXiv:1402.4686.
  • Pemantle, Robin. A survey of random processes with reinforcement. Probab. Surv. 4 (2007), 1--79. MR2282181
  • Robbins, Herbert; Monro, Sutton. A stochastic approximation method. Ann. Math. Statistics 22, (1951). 400--407. MR0042668
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