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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 30 open journal systems 


Central Limit Theorem For The Excited Random Walk In Dimension d≥2

Jean Berard, Université de Lyon
Alejandro Ramirez, Pontificia Universidad Catolica de Chile


Abstract
We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension d≥2


Full text: PDF

Pages: 303-314

Published on: October 3, 2007


Bibliography
  1. Benjamini, Itai; Wilson, David B. Excited random walk. Electron. Comm. Probab. 8 (2003), 86--92 (electronic). MR1987097 (2004b:60120)
  2. Bolthausen, E. On the volume of the Wiener sausage. Ann. Probab. 18 (1990), no. 4, 1576--1582. MR1071810 (92e:60151)
  3. Bousquet-Mélou, Mireille; Schaeffer, Gilles. Walks on the slit plane. Probab. Theory Related Fields 124 (2002), no. 3, 305--344. MR1939650 (2003h:60013)
  4. Davis, Burgess. Weak limits of perturbed random walks and the equation $Ysb t=Bsb t+alphasup{Ysb scolon sleq t}+betainf{Ysb scolon sleq t}$. Ann. Probab. 24 (1996), no. 4, 2007--2023. MR1415238 (97m:60021)
  5. Davis, Burgess. Brownian motion and random walk perturbed at extrema. Probab. Theory Related Fields 113 (1999), no. 4, 501--518. MR1717528 (2001k:60030)
  6. Donsker, M. D.; Varadhan, S. R. S. On the number of distinct sites visited by a random walk. Comm. Pure Appl. Math. 32 (1979), no. 6, 721--747. MR0539157 (81j:60080)
  7. Benjamini, Itai; Wilson, David B. Excited random walk. Electron. Comm. Probab. 8 (2003), 86--92 (electronic). MR1987097 (2004b:60120)
  8. Gady Kozma. Excited random walk in two dimensions has linear speed. arXiv: math/0512535, 2005, 2005.
  9. Mountford, Thomas; Pimentel, Leandro P. R.; Valle, Glauco. On the speed of the one-dimensional excited random walk in the transient regime. ALEA Lat. Am. J. Probab. Math. Stat. 2 (2006), 279--296 (electronic). MR2285733
  10. Perman, Mihael; Werner, Wendelin. Perturbed Brownian motions. Probab. Theory Related Fields 108 (1997), no. 3, 357--383. MR1465164 (98i:60081)
  11. Sznitman, Alain-Sol. Long time asymptotics for the shrinking Wiener sausage. Comm. Pure Appl. Math. 43 (1990), no. 6, 809--820. MR1059329 (92e:60152)
  12. Sznitman, Alain-Sol. Slowdown estimates and central limit theorem for random walks in random environment. J. Eur. Math. Soc. (JEMS) 2 (2000), no. 2, 93--143. MR1763302 (2001j:60192)
  13. Sznitman, Alain-Sol; Zerner, Martin. A law of large numbers for random walks in random environment. Ann. Probab. 27 (1999), no. 4, 1851--1869. MR1742891 (2001f:60116)
  14. Remco van den Hofstad and Mark Holmes. An expansion for self-interacting random walks. arXiv:0706.0614, 2006.
  15. Volkov, Stanislav. Excited random walk on trees. Electron. J. Probab. 8 (2003), no. 23, 15 pp. (electronic). MR2041824 (2005a:60113)
  16. Zerner, Martin P. W. Multi-excited random walks on integers. Probab. Theory Related Fields 133 (2005), no. 1, 98--122. MR2197139 (2006k:60178)
  17. Zerner, Martin P. W. Recurrence and transience of excited random walks on $Bbb Zsp d$ and strips. Electron. Comm. Probab. 11 (2006), 118--128 (electronic). MR2231739 (2007g:60123)
















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Electronic Communications in Probability. ISSN: 1083-589X