Superdiffusivity in first-passage percolation

Probability Theory and Related Fields

Volumn 106, Issue 4, 1996, Pages 559-591

  Licea, C ^c   Newman, C M ^a   Piza, M S T ^b  

^a NEW YORK UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Standard and Poor's   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444460424     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050075     Document Type: Article

References (22)

1. K. Alexander: Approximation of subadditive functions and convergence rates in limiting-shape results, Ann. Probab., to appear.
2. M. Aizenman, J. Wehr: Rounding effects of quenched randomness on first-order phase transitions, Commun. Math. Phys. 130 (1990) 489-528.
3. J. van den Berg, H. Kesten: Inequalities for the time constant in first-passage percolation, Ann. Appl. Probab. 3 (1993) 56-80.
4. J. Cook, B. Derrida: Directed polymers in a random medium: l/d expansion and the n-tree approximation, J. Phys. A.. Math. Gen. 23 (1990) 1523-1554.
5. T. Halpin-Healy: Diverse manifolds in random media, Phys. Rev. Lett. 62 (1989) 442-445.
6. D. A. Huse, C. L. Henley: Pinning and roughening of domain walls in Ising systems due to random impurities, Phys. Rev. Lett. 54 (1985) 2708-2711.
7. D. A. Huse, C. L. Henley, D. S. Fisher: Phys. Rev. Lett. 55 (1985) 2924-2924.
8. J.M. Hammersley, D.J.A. Welsh: First-passage percolation, subadditive processes, stochastic networks and generalized renewal theory, pp.61-110 in Bernoulli, Bayes, Laplace Anniversary Volume (J. Neyman, L. Lecam, eds.), Springer-Verlag, Berlin, 1965.
9. M. Kardar: Roughening by impurities at finite temperatures, Phys. Rev. Lett. 55 (1985) 2923-2923.
10. H. Kesten: Aspects of first passage percolation, pp.125-264 in Lecture Notes in Mathematics, vol. 1180, Springer-Verlag (1986), Berlin.
11. H. Kesten: Percolation theory and first-passage percolation, Ann. Probab. 15 (1987) 1231-1271.
12. H. Kesten: On the speed of convergence in first-passage percolation, Ann. Appl. Probab. 3 (1993) 296-338.
13. J. M. Kim, J. M. Kosterlitz: Growth in a restricted solid-on-solid model, Phys. Rev. Lett. 62 (1989) 2289-2292.
14. M. Kardar, G. Parisi, Y.-C. Zhang: Dynamic scaling of growing interfaces, Phys. Rev. Lett. 56 (1986) 889-892.
15. J. Krug, H. Spohn: Kinetic roughening of growing surfaces, pp. 479-582 in Solids far from equilibrium: growth, morphology and defects (C. Godrèche, ed.), Cambridge University Press, 1991.
16. M. Kardar, Y.-C. Zhang: Scaling of directed polymers in random media, Phys. Rev. Lett. 58 (1987) 2087-2090.
17. C. Licea, C. M. Newman: Geodesics in two-dimensional first-passage percolation, Ann. Probab. 24 (1996), to appear.
18. C. M. Newman: A surface view of first-passage percolation, pp. 1017-1023 in Proceedings of the International Congress of Mathematicians Vol. II (S. D. Chatterji, ed.), Birkhäuser, Basel, 1995.
19. C. M. Newman, M. S. T. Piza: Divergence of shape fluctuations in two dimensions, Ann. Probab. 23 (1995) 977-1005.
20. T. Natterman, W. Renz: Interface roughening due to random impurities at low temperatures, Phys. Rev. B 38 (1988) 5184-5187.
21. J. Wehr, M. Aizenman: Fluctuations of extensive functions of quenched random couplings, J. Stat. Phys. 60 (1990) 287-306.
22. D. E. Wolf, J. Kertész: Surface with exponents for three and four dimensional Eden growth, Europhys. Lett. 1 (1987) 651-656.