@article{AIHPB_1998__34_5_567_0,
author = {Boivin, Daniel},
title = {Ergodic theorems for surfaces with minimal random weights},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
volume = {34},
year = {1998},
pages = {567-599},
mrnumber = {1641662},
zbl = {0910.60078},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPB_1998__34_5_567_0}
}
Boivin, Daniel. Ergodic theorems for surfaces with minimal random weights. Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) pp. 567-599. http://gdmltest.u-ga.fr/item/AIHPB_1998__34_5_567_0/
[1] and , Ergodic theorems for superadditive processes, J. Reine Angew. Math., Vol. 323, 1981, pp. 53-67. | MR 611442 | Zbl 0453.60039
[2] , , , and , On a sharp transition from area law to perimeter law in a system of random surfaces, Comm. Math. Phys., Vol. 92, 1983, pp. 19-69. | MR 728447 | Zbl 0529.60099
[3] and , Asymptotic Expansions of Integrals, Dover Publications, 1975. | MR 863284 | Zbl 0327.41027
[4] , Weak convergence for reversible random walks in a random environment, Ann. Probab., Vol. 21, 1993, pp. 1427-1440. | MR 1235423 | Zbl 0783.60067
[5] , First-passage percolation: the stationary case, Probab. Th. Rel. Fields, Vol. 86, 1990, pp. 491-499. | MR 1074741 | Zbl 0685.60103
[6] , Ergodic theory and translation invariant operators, Proc. Nat. Acad. Sci. USA, Vol. 59, 1968, pp. 349-353. | MR 227354 | Zbl 0185.21806
[7] and , Some limit theorems for percolation processes with necessary and sufficient conditions, Ann. Probab., Vol. 9, 1981, pp. 583-603. | MR 624685 | Zbl 0462.60012
[8] and , Counterexamples in Ergodic Theory and Number Theory, Math. Ann., Vol. 245, 1979, pp. 185-197. | MR 553340 | Zbl 0398.28021
[9] , Thèse de doctorat, Université de Bretagne Occidentale, 1994.
[10] , Lecture Notes on Particule Systems and Percolation, Wads-worth & Brooks/Cole, 1988. | Zbl 0659.60129
[11] and , Bounds for effective parameters of heterogeneous media by analytic continuation, Comm. Math. Phys., Vol. 90, 1983, pp. 473-491. | MR 719428
[12] and , First-passage percolation, network flows and electrical resistances, Z. Wahrsch. verw. Gebiete, Vol. 66, 1984, pp. 335-366. | MR 751574 | Zbl 0525.60098
[13] and , Asymptotic shapes for stationary first passage percolation, Ann. Probab., Vol. 23, 1995, pp. 1511-1522. | MR 1379157 | Zbl 0852.60104
[14] , A simple proof of the ergodic theorem using non-standard analysis, Israel J. Math., Vol. 42, 1982, pp. 284-290. | MR 682311 | Zbl 0499.28011
[15] , Ergodic theory and subshifts of finite type. In Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford University Press, 1991. | MR 1130172 | Zbl 0755.58033
[16] , Surfaces with minimal random weights and maximal flows: A higher dimensional version of first-passage percolation, Illinois J. Math., Vol. 31, 1987, pp. 99-166. | MR 869483 | Zbl 0591.60096
[17] , Percolation theory and first-passage percolation, Ann. Probab., Vol. 15, 1987, pp. 1231-1271. | MR 905330 | Zbl 0629.60103
[18] , Aspects of first-passage percolation, Lecture Notes in Math., Vol. 1180, Springer, New York, 1986, pp. 125-264. | MR 876084 | Zbl 0602.60098
[19] , The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys, Vol. 40, 1985, pp. 73-145. | Zbl 0615.60063
[20] , Ergodic Theorems, de Gruyter Studies in Mathematics 6, de Gruyter, Berlin, 1985. | MR 797411 | Zbl 0575.28009
[21] , Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. of the AMS, Vol. 69, 1963, pp. 766-770. | MR 155146 | Zbl 0143.34701
[22] , Random growth in a tesselation, Proc. Cambridge Philos. Soc., Vol. 74, 1973, pp. 515-528. | MR 329079 | Zbl 0295.62094
[23] , Maximal functions and Fourier transforms, Duke Math. J., Vol. 53, 1986, pp. 395-404. | MR 850542 | Zbl 0612.42008
[24] , Applications of Functional Analysis in Mathematical Physics. Translations of Mathematical Monographs, American Mathematical Society, Vol. 7, 1963. | MR 165337 | Zbl 0123.09003
[25] and , Problems in harmonic analysis related to curvature, Bulletin of the AMS, Vol. 84, 1978, pp. 1239-1295. | MR 508453 | Zbl 0393.42010
[26] , Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press, 1993. | MR 1232192 | Zbl 0821.42001
[27] , The ergodic theorem, Duke Math. J., Vol. 5, 1939, pp. 1-18. | JFM 65.0516.04 | Zbl 0021.23501