Marches pseudo-aléatoires issues de substitutions : aspects statistiques
Jeannet, B. ; Huillet, T. ; Choukri, K.
Annales de l'I.H.P. Physique théorique, Tome 67 (1997), p. 77-89 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1997-01-01
@article{AIHPA_1997__67_1_77_0,
     author = {Jeannet, B. and Huillet, T. and Choukri, K.},
     title = {Marches pseudo-al\'eatoires issues de substitutions : aspects statistiques},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {67},
     year = {1997},
     pages = {77-89},
     mrnumber = {1463006},
     zbl = {0896.60079},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPA_1997__67_1_77_0}
}

Jeannet, B.; Huillet, T.; Choukri, K. Marches pseudo-aléatoires issues de substitutions : aspects statistiques. Annales de l'I.H.P. Physique théorique, Tome 67 (1997) pp. 77-89. http://gdmltest.u-ga.fr/item/AIHPA_1997__67_1_77_0/

[1] J.-P. Allouche et M. Mendès France, Automata and automatic sequences. Beyond quasicrystals, Éd. F. AXEL, D. GRATIAS, Springer, Les Éditions de Physique, 1995, p. 293-367. | MR 1420422 | Zbl 0881.11026

[2] F. Barnsley, J.H. Elton et D. Hardin, Recurrent iterated functions systems., Constr. Approx., vol. 5, 1989, p. 3-39. | MR 982722 | Zbl 0659.60045

[3] F. Dekking, Substitutions, branching processes and fractal sets. Fractal Geometry and Analysis, Ed. J. Bélair and S. Dubuc. Kluwer Academic Pub., 1991, p. 99-119. | MR 1140721 | Zbl 0739.58039

[4] F. Dekking, Recurrent sets, Adv. in Math., vol. 44, 1982, p. 78-104. | MR 654549 | Zbl 0495.51017

[5] F. Dekking, M. Mendès France, et A. Van Der Poorten, Folds! (I,II,III), The Mathematical Intelligencer-Springer-Verlag, vol. 4, 1982, number 3 et 4. | MR 684028

[6] F. Dekking, Marches automatiques, Journal de théorie des nombres de Bordeaux, vol. 5, 1993, p. 93-100. | Numdam | MR 1251229 | Zbl 0795.11011

[7] R.S. Ellis, Entropy, large deviations and statistical mechanics, New York, Springer, 1985. | MR 793553 | Zbl 0566.60097

[8] T. Huillet et B. Jeannet, On statistical aspects of deterministic tree-like fractals, J. of Physics A. Math. Gen., vol. 27, 1994, p. 1191-1198. | MR 1269043 | Zbl 0803.60098

[9] T. Huillet et B. Jeannet, On a class of skewed self-similar and hyperbolic fractals, J. of Mathematical Physics, vol. 35, (12), 1994, p. 6510-6524. | MR 1303059 | Zbl 0820.60072

[10] M. Lothaire, Combinatorics on words, Encyclopedia of Mathematics and its applications, Addison-Wesley Publishing Company, 1983. | MR 675953 | Zbl 0514.20045

[11] R.D. Mauldin et S.C. Williams, Hausdorff dimensions in graph directed constructions, Trans. Amer. Math. Soc., vol. 309, 1988, p. 811-829. | MR 961615 | Zbl 0706.28007

[12] G. Michon et J. Peyrière, Thermodynamique des ensembles de Cantor autosimilaires, Chinese Annals of Math., vol. 15B, 1994, p. 253-272. | MR 1303208 | Zbl 0848.54023

[13] J. Peyrière, Substitutions aléatoires itérées, Séminaire de théorie des nombres de Bordeaux, vol. 80-81, 1981, p. 1701-1709. | Zbl 0474.60070

[14] M. Queffélec, Substitution dynamical systems-spectral analysis, Lecture Notes in Mathematics, vol. 1294, 1987. | MR 924156 | Zbl 0642.28013

[15] D. Ruelle, Thermodynamic formalism, Encyclopedia of Mathematics and its applications, Addison-Wesley Publishing Company, Massachusetts, 1978. | MR 511655 | Zbl 0401.28016

[16] Z.-X. Wen et Z.-Y. Wen, Mots infinis et produits de matrices à coefficients polynômiaux, RAIRO Info. Théor. et Applic., vol. 26, 1992, p. 319-343. | Numdam | MR 1173173 | Zbl 0758.11016

[17] Z.-X. Wen, Marches sur les arbres homogènes suivant une suite substitutive, Thèse, Université Paris-Sud, Juin, 1991.