@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}, pages = {567--599}, publisher = {Gauthier-Villars}, volume = {34}, number = {5}, year = {1998}, mrnumber = {1641662}, zbl = {0910.60078}, language = {en}, url = {http://www.numdam.org/item/AIHPB_1998__34_5_567_0/} }
TY - JOUR AU - Boivin, Daniel TI - Ergodic theorems for surfaces with minimal random weights JO - Annales de l'I.H.P. Probabilités et statistiques PY - 1998 SP - 567 EP - 599 VL - 34 IS - 5 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPB_1998__34_5_567_0/ LA - en ID - AIHPB_1998__34_5_567_0 ER -
Boivin, Daniel. Ergodic theorems for surfaces with minimal random weights. Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) no. 5, pp. 567-599. http://www.numdam.org/item/AIHPB_1998__34_5_567_0/
[1] Ergodic theorems for superadditive processes, J. Reine Angew. Math., Vol. 323, 1981, pp. 53-67. | MR | Zbl
and ,[2] 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 | Zbl
, , , and ,[3] Asymptotic Expansions of Integrals, Dover Publications, 1975. | MR | Zbl
and ,[4] Weak convergence for reversible random walks in a random environment, Ann. Probab., Vol. 21, 1993, pp. 1427-1440. | MR | Zbl
,[5] First-passage percolation: the stationary case, Probab. Th. Rel. Fields, Vol. 86, 1990, pp. 491-499. | MR | Zbl
,[6] Ergodic theory and translation invariant operators, Proc. Nat. Acad. Sci. USA, Vol. 59, 1968, pp. 349-353. | MR | Zbl
,[7] Some limit theorems for percolation processes with necessary and sufficient conditions, Ann. Probab., Vol. 9, 1981, pp. 583-603. | MR | Zbl
and ,[8] Counterexamples in Ergodic Theory and Number Theory, Math. Ann., Vol. 245, 1979, pp. 185-197. | MR | Zbl
and ,[9] Thèse de doctorat, Université de Bretagne Occidentale, 1994.
,[10] Lecture Notes on Particule Systems and Percolation, Wads-worth & Brooks/Cole, 1988. | Zbl
,[11] Bounds for effective parameters of heterogeneous media by analytic continuation, Comm. Math. Phys., Vol. 90, 1983, pp. 473-491. | MR
and ,[12] First-passage percolation, network flows and electrical resistances, Z. Wahrsch. verw. Gebiete, Vol. 66, 1984, pp. 335-366. | MR | Zbl
and ,[13] Asymptotic shapes for stationary first passage percolation, Ann. Probab., Vol. 23, 1995, pp. 1511-1522. | MR | Zbl
and ,[14] A simple proof of the ergodic theorem using non-standard analysis, Israel J. Math., Vol. 42, 1982, pp. 284-290. | MR | Zbl
,[15] Ergodic theory and subshifts of finite type. In Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford University Press, 1991. | MR | Zbl
,[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 | Zbl
,[17] Percolation theory and first-passage percolation, Ann. Probab., Vol. 15, 1987, pp. 1231-1271. | MR | Zbl
,[18] Aspects of first-passage percolation, Lecture Notes in Math., Vol. 1180, Springer, New York, 1986, pp. 125-264. | MR | Zbl
,[19] The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys, Vol. 40, 1985, pp. 73-145. | Zbl
,[20] Ergodic Theorems, de Gruyter Studies in Mathematics 6, de Gruyter, Berlin, 1985. | MR | Zbl
,[21] Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. of the AMS, Vol. 69, 1963, pp. 766-770. | MR | Zbl
,[22] Random growth in a tesselation, Proc. Cambridge Philos. Soc., Vol. 74, 1973, pp. 515-528. | MR | Zbl
,[23] Maximal functions and Fourier transforms, Duke Math. J., Vol. 53, 1986, pp. 395-404. | MR | Zbl
,[24] Applications of Functional Analysis in Mathematical Physics. Translations of Mathematical Monographs, American Mathematical Society, Vol. 7, 1963. | MR | Zbl
,[25] Problems in harmonic analysis related to curvature, Bulletin of the AMS, Vol. 84, 1978, pp. 1239-1295. | MR | Zbl
and ,[26] Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press, 1993. | MR | Zbl
,[27] The ergodic theorem, Duke Math. J., Vol. 5, 1939, pp. 1-18. | JFM | Zbl
,