Ergodic theorems for surfaces with minimal random weights
Annales de l'I.H.P. Probabilités et statistiques (1998)
- Volume: 34, Issue: 5, page 567-599
- ISSN: 0246-0203
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topBoivin, Daniel. "Ergodic theorems for surfaces with minimal random weights." Annales de l'I.H.P. Probabilités et statistiques 34.5 (1998): 567-599. <http://eudml.org/doc/77614>.
@article{Boivin1998,
author = {Boivin, Daniel},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {first-passage percolation; moment condition},
language = {eng},
number = {5},
pages = {567-599},
publisher = {Gauthier-Villars},
title = {Ergodic theorems for surfaces with minimal random weights},
url = {http://eudml.org/doc/77614},
volume = {34},
year = {1998},
}
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
PB - Gauthier-Villars
VL - 34
IS - 5
SP - 567
EP - 599
LA - eng
KW - first-passage percolation; moment condition
UR - http://eudml.org/doc/77614
ER -
References
top- [1] M.A. Akcoglu and U. Krengel, Ergodic theorems for superadditive processes, J. Reine Angew. Math., Vol. 323, 1981, pp. 53-67. Zbl0453.60039MR611442
- [2] M. Aizenman, J.T. Chayes, L. Chayes, J. Frölich and L. Russo, 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. Zbl0529.60099MR728447
- [3] N. Bleistein and R.A. Handelsman, Asymptotic Expansions of Integrals, Dover Publications, 1975. Zbl0327.41027MR863284
- [4] D. Boivin, Weak convergence for reversible random walks in a random environment, Ann. Probab., Vol. 21, 1993, pp. 1427-1440. Zbl0783.60067MR1235423
- [5] D. Boivin, First-passage percolation: the stationary case, Probab. Th. Rel. Fields, Vol. 86, 1990, pp. 491-499. Zbl0685.60103MR1074741
- [6] A. Calderon, Ergodic theory and translation invariant operators, Proc. Nat. Acad. Sci. USA, Vol. 59, 1968, pp. 349-353. Zbl0185.21806MR227354
- [7] J.T. Cox and R. Durrett, Some limit theorems for percolation processes with necessary and sufficient conditions, Ann. Probab., Vol. 9, 1981, pp. 583-603. Zbl0462.60012MR624685
- [8] A. Del Junco and J. Rosenblatt, Counterexamples in Ergodic Theory and Number Theory, Math. Ann., Vol. 245, 1979, pp. 185-197. Zbl0398.28021MR553340
- [9] J. Depauw, Thèse de doctorat, Université de Bretagne Occidentale, 1994.
- [10] R. Durrett, Lecture Notes on Particule Systems and Percolation, Wads-worth & Brooks/Cole, 1988. Zbl0659.60129
- [11] K. Golden and G. Papanicolaou, Bounds for effective parameters of heterogeneous media by analytic continuation, Comm. Math. Phys., Vol. 90, 1983, pp. 473-491. MR719428
- [12] G. Grimmett and H. Kesten, First-passage percolation, network flows and electrical resistances, Z. Wahrsch. verw. Gebiete, Vol. 66, 1984, pp. 335-366. Zbl0525.60098MR751574
- [13] O. Haggstrom and R. Meester, Asymptotic shapes for stationary first passage percolation, Ann. Probab., Vol. 23, 1995, pp. 1511-1522. Zbl0852.60104MR1379157
- [14] Y. Kamae, A simple proof of the ergodic theorem using non-standard analysis, Israel J. Math., Vol. 42, 1982, pp. 284-290. Zbl0499.28011MR682311
- [15] M. Keane, Ergodic theory and subshifts of finite type. In Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford University Press, 1991. Zbl0755.58033MR1130172
- [16] H. Kesten, 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. Zbl0591.60096MR869483
- [17] H. Kesten, Percolation theory and first-passage percolation, Ann. Probab., Vol. 15, 1987, pp. 1231-1271. Zbl0629.60103MR905330
- [18] H. Kesten, Aspects of first-passage percolation, Lecture Notes in Math., Vol. 1180, Springer, New York, 1986, pp. 125-264. Zbl0602.60098MR876084
- [19] S.M. Kozlov, The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys, Vol. 40, 1985, pp. 73-145. Zbl0615.60063
- [20] U. Krengel, Ergodic Theorems, de Gruyter Studies in Mathematics6, de Gruyter, Berlin, 1985. Zbl0575.28009MR797411
- [21] W. Littman, Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. of the AMS, Vol. 69, 1963, pp. 766-770. Zbl0143.34701MR155146
- [22] D. Richardson, Random growth in a tesselation, Proc. Cambridge Philos. Soc., Vol. 74, 1973, pp. 515-528. Zbl0295.62094MR329079
- [23] J.L. Rubio De Francia, Maximal functions and Fourier transforms, Duke Math. J., Vol. 53, 1986, pp. 395-404. Zbl0612.42008MR850542
- [24] S.L. Sobolev, Applications of Functional Analysis in Mathematical Physics. Translations of Mathematical Monographs, American Mathematical Society, Vol. 7, 1963. Zbl0123.09003MR165337
- [25] E.M. Stein and S. Wainger, Problems in harmonic analysis related to curvature, Bulletin of the AMS, Vol. 84, 1978, pp. 1239-1295. Zbl0393.42010MR508453
- [26] E.M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton University Press, 1993. Zbl0821.42001MR1232192
- [27] N. Wiener, The ergodic theorem, Duke Math. J., Vol. 5, 1939, pp. 1-18. Zbl0021.23501JFM65.0516.04
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