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

  1. Asselah A., Gaudilliere A. From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models, arXiv:1009.2838.
  2. Asselah A., Gaudilliere A. Sub-logarithmic fluctuations for internal DLA, arXiv:1011.4592.
  3. Ben Arous, Gérard; Quastel, Jeremy; Ramírez, Alejandro F. Internal DLA in a random environment. Ann. Inst. H. Poincaré Probab. Statist. 39 (2003), no. 2, 301--324. MR1962779 (2003m:60285)
  4. Benaïm, Michel. Dynamics of stochastic approximation algorithms. Séminaire de Probabilités, XXXIII, 1--68, Lecture Notes in Math., 1709, Springer, Berlin, 1999. MR1767993 (2001d:62081)
  5. Benjamini, Itai; Wilson, David B. Excited random walk. Electron. Comm. Probab. 8 (2003), 86--92 (electronic). MR1987097 (2004b:60120)
  6. Blachère, Sébastien; Brofferio, Sara. Internal diffusion limited aggregation on discrete groups having exponential growth. Probab. Theory Related Fields 137 (2007), no. 3-4, 323--343. MR2278460 (2008b:60210)
  7. Lawler, Gregory F.; Bramson, Maury; Griffeath, David. Internal diffusion limited aggregation. Ann. Probab. 20 (1992), no. 4, 2117--2140. MR1188055 (94a:60105)
  8. Chaumont, L.; Doney, R. A. Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion. Probab. Theory Related Fields 113 (1999), no. 4, 519--534. MR1717529 (2000k:60162)
  9. Diaconis P., Fulton W. A growth model, a game, an algebra, Lagrange inversion, and characteristic classes, Rend. Sem. Mat. Univ. Politec. Torino 49, (1991), 95--119 (1993), Commutative algebra and algebraic geometry, II (Italian) (Turin, 1990).
  10. Dolgopyat D. Central limit theorem for excited random walk in the recurrent regime, preprint,http://www.math.umd.edu/~dmitry/papers.html
  11. Duflo, Marie. Algorithmes stochastiques.(French) [Stochastic algorithms] Mathématiques & Applications (Berlin) [Mathematics & Applications], 23. Springer-Verlag, Berlin, 1996. xiv+319 pp. ISBN: 3-540-60699-8 MR1612815 (99e:62141)
  12. Enriquez, N.; Lucas, C.; Simenhaus, F. The arcsine law as the limit of the internal DLA cluster generated by Sinai's walk. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010), no. 4, 991--1000. MR2744882 (Review)
  13. Gravner, Janko; Quastel, Jeremy. Internal DLA and the Stefan problem. Ann. Probab. 28 (2000), no. 4, 1528--1562. MR1813833 (2001m:60222)
  14. Jerison D., Levine L., Sheffield S.: Logarithmic fluctuations for internal DLA, arXiv:1010.2483.
  15. Jerison D., Levine L., Sheffield S.: Internal DLA in higher dimensions, arXiv:1012.3453.
  16. Jerison D., Levine L., Sheffield S.: Internal DLA and the Gaussian free field}, arXiv:1101.0596.
  17. Kosygina, Elena; Zerner, Martin P. W. Positively and negatively excited random walks on integers, with branching processes. Electron. J. Probab. 13 (2008), no. 64, 1952--1979. MR2453552 (2009m:60231)
  18. Lawler G.: Subdiffusive fluctuations for internal diffusion limited aggregation, Ann. Probab. 23, (1995), 71--86.
  19. Le Gall J.-F.:L''equation stochastique $Y_t=B_T+alpha M_t^Y + beta I_t^Y$ comme limite des 'equations de Norris--Rogers--Williams, (French) (1986), unpublished note.
  20. Le Gall, Jean-François; Yor, Marc. Enlacements du mouvement brownien autour des courbes de l'espace.(French) [Brownian windings around space curves] Trans. Amer. Math. Soc. 317 (1990), no. 2, 687--722. MR0946219 (90e:60099)
  21. Levine, Lionel; Peres, Yuval. Scaling limits for internal aggregation models with multiple sources. J. Anal. Math. 111 (2010), 151--219. MR2747064
  22. Shellef, Eric. IDLA on the supercritical percolation cluster. Electron. J. Probab. 15 (2010), no. 24, 723--740. MR2650780 (2011e:60230)
  23. Perman, Mihael; Werner, Wendelin. Perturbed Brownian motions. Probab. Theory Related Fields 108 (1997), no. 3, 357--383. MR1465164 (98i:60081)
  24. Zerner, Martin P. W. Multi-excited random walks on integers. Probab. Theory Related Fields 133 (2005), no. 1, 98--122. MR2197139 (2006k:60178)
  25. Walters, Peter. An introduction to ergodic theory.Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982. ix+250 pp. ISBN: 0-387-90599-5 MR0648108 (84e:28017)
Bookmark and Share


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