no. 5
Gaussian lower bounds for random walks from elliptic regularity
Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) no. 5, pp. 605-630. 
@article{AIHPB_1999__35_5_605_0,
     author = {Auscher, Pascal and Coulhon, Thierry},
     title = {Gaussian lower bounds for random walks from elliptic regularity},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {605--630},
     publisher = {Gauthier-Villars},
     volume = {35},
     number = {5},
     year = {1999},
     mrnumber = {1705682},
     zbl = {0933.60047},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1999__35_5_605_0/}
}
TY  - JOUR
AU  - Auscher, Pascal
AU  - Coulhon, Thierry
TI  - Gaussian lower bounds for random walks from elliptic regularity
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1999
SP  - 605
EP  - 630
VL  - 35
IS  - 5
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPB_1999__35_5_605_0/
LA  - en
ID  - AIHPB_1999__35_5_605_0
ER  - 
%0 Journal Article
%A Auscher, Pascal
%A Coulhon, Thierry
%T Gaussian lower bounds for random walks from elliptic regularity
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1999
%P 605-630
%V 35
%N 5
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPB_1999__35_5_605_0/
%G en
%F AIHPB_1999__35_5_605_0
Auscher, Pascal; Coulhon, Thierry. Gaussian lower bounds for random walks from elliptic regularity. Annales de l'I.H.P. Probabilités et statistiques, Tome 35 (1999) no. 5, pp. 605-630. http://archive.numdam.org/item/AIHPB_1999__35_5_605_0/

[1] P. Auscher, Regularity theorems and heat kernel for elliptic operators, J. London Math. Soc. 2 (54) (1996) 284-296. | MR | Zbl

[2] M. Christ, Temporal regularity for random walk on discrete nilpotent groups, J. Fourier Analysis Appl. (Kahane special issue) (1995) 141-151. | MR | Zbl

[3] T. Coulhon, Analysis on graphs with regular volume growth, Symposia Math., to appear. | Zbl

[4] T. Coulhon and A. Grigor'Yan, Random walks on graphs with regular volume growth, G.A.F.A. 8 (1998) 656-701. | MR | Zbl

[5] T. Coulhon and L. Saloff-Coste, Minorations pour les chaînes de Markov unidimensionnelles, Probab. Theory Related Fields 97 (1993) 423-431. | MR | Zbl

[6] E. De Giorgi, Sulla differenziabilita e l'analiticita delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat. 3 (3) (1957) 25- 43. | MR | Zbl

[7] T. Delmotte, Inégalité de Harnack elliptique sur les graphes, Coll. Math. 72 (1) (1997) 19-37. | MR | Zbl

[8] T. Delmotte, Parabolic Harnack inequality and estimates of Markov chains on graphs, Rev. Mat. Iberoam. 15 (1) (1999) 181-232. | MR | Zbl

[9] T. Delmotte, Versions discrètes de l'inégalité de Harnack, thesis, University of Cergy-Pontoise, 1997.

[10] M. Giaquinta, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton Univ. Press, 1983. | MR | Zbl

[11] M. Giaquinta, Introduction to Regularity Theory for Nonlinear Elliptic Systems, Birkhaüser, 1993. | MR | Zbl

[12] A. Grigor'Yan, The heat equation on non-compact Riemannian manifolds, Matem. Sbornik 182 (1) (1991) 55-87 (in Russian); English translation: Math. USSR Sb. 72 (1) (1992) 47-77. | MR | Zbl

[13] P. Hajlasz and P. Koskela, Sobolev met Poincaré, to appear in Memoirs of the Amer. Math. Soc. | MR | Zbl

[14] W. Hebisch and L. Saloff-COSTE, Gaussian estimates for Markov chains and random walks on groups, Ann. Probab. 21 (1993) 673-709. | MR | Zbl

[15] C. Morrey, Multiple Integrals in the Calculus of Variations, Springer, 1966. | MR | Zbl

[16] E. Russ, Riesz transforms on graphs for 1 ≤ p ≤ 2, Math. Scand., to appear. | MR | Zbl

[17] L. Saloff-Coste, A note on Poincaré, Sobolev, and Harnack inequalities, Duke Math. J., I.M.R.N. 2 (1992) 27-38. | MR | Zbl

[18] L. Saloff-Coste, Parabolic Harnack inequality for divergence form second order differential operators, Potential Analysis 4 (4) (1995) 429-467. | MR | Zbl