Comptes Rendus
no. 11
Probability theory
The infinite differentiability of the speed for excited random walks
[La vitesse d'une marche aléatoire excitée est infiniment différentiable]

Présenté par : 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.

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).

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.10.012

Cong-Dan Pham 1

1 Duy Tan University, Da Nang, Viet Nam 
@article{CRMATH_2016__354_11_1119_0,
     author = {Cong-Dan Pham},
     title = {The infinite differentiability of the speed for excited random walks},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1119--1123},
     publisher = {Elsevier},
     volume = {354},
     number = {11},
     year = {2016},
     doi = {10.1016/j.crma.2016.10.012},
     language = {en},
}
TY  - JOUR
AU  - Cong-Dan Pham
TI  - The infinite differentiability of the speed for excited random walks
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 1119
EP  - 1123
VL  - 354
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crma.2016.10.012
LA  - en
ID  - CRMATH_2016__354_11_1119_0
ER  - 
%0 Journal Article
%A Cong-Dan Pham
%T The infinite differentiability of the speed for excited random walks
%J Comptes Rendus. Mathématique
%D 2016
%P 1119-1123
%V 354
%N 11
%I Elsevier
%R 10.1016/j.crma.2016.10.012
%G en
%F CRMATH_2016__354_11_1119_0
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

Cité par Sources :

Commentaires - Politique