Comptes Rendus
no. 11
Probability theory
The infinite differentiability of the speed for excited random walks

Presented by: the Editorial Board

Cong-Dan Pham1
1 Duy Tan University, Da Nang, Viet Nam
Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1119-1123.

We prove that the speed of the excited random walk is infinitely differentiable with respect to the bias parameter in (0,1) for the dimension d⩾2.

Nous montrons que la vitesse d'une marche aléatoire excitée sur Zd, d⩾2, est infiniment différentiable par rapport au paramètre de biais dans (0,1).

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.10.012

Cong-Dan Pham 1

1 Duy Tan University, Da Nang, Viet Nam 
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Cong-Dan Pham. The infinite differentiability of the speed for excited random walks. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1119-1123. doi : 10.1016/j.crma.2016.10.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.10.012/

[1] A.-L. Basdevant; A. Singh On the speed of a cookie random walk, Probab. Theory Relat. Fields, Volume 141 (2008) no. 3–4, pp. 625-645

[2] I. Benjamini; D. Wilson Excited random walk, Electron. Commun. Probab., Volume 8 (2003) no. 9, pp. 86-92

[3] J. Bérard; A. Ramírez Central limit theorem for the excited random walk in dimension d⩾2, Electron. Commun. Probab., Volume 12 (2007) no. 30, pp. 303-314

[4] E. Bolthausen; A.-S. Sznitman; O. Zeitouni Cut points and diffusive random walks in random environment, Ann. Inst. Henri Poincaré Probab. Stat., Volume 39 (2003), pp. 527-555

[5] M. Holmes Excited against the tide: a random walk with competing drifts, Ann. Inst. Henri Poincaré Probab. Stat., Volume 48 (2012), pp. 745-773

[6] M. Menshikov; S. Popov On range and local time of many-dimensional submartingales, J. Theor. Probab., Volume 27 (2014) no. 2, pp. 601-617

[7] M. Menshikov; S. Popov; A.F. Ramírez; M. Vachkovskaia On a general many-dimensional excited random walk, Ann. Probab., Volume 40 (2012) no. 5, pp. 2106-2130

[8] C.D. Pham Monotonicity and regularity of the speed for excited random walks in higher dimensions, Electron. J. Probab., Volume 20 (2015), p. 72:1-72:25

[9] M. Zerner Multi-excited random walks on integers, Probab. Theory Relat. Fields, Volume 133 (2005) no. 1, pp. 98-122

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