On large deviation regimes for random media models
M. Cranston, D. Gauthier, and T. S. Mountford
Source: Ann. Appl. Probab. Volume 19, Number 2
(2009), 826-862.
Abstract
The focus of this article is on the different behavior of large deviations of random subadditive functionals above the mean versus large deviations below the mean in two random media models. We consider the point-to-point first passage percolation time an on ℤd and a last passage percolation time Zn. For these functionals, we have limn→∞an/n=ν and limn→∞Zn/n=μ. Typically, the large deviations for such functionals exhibits a strong asymmetry, large deviations above the limiting value are radically different from large deviations below this quantity. We develop robust techniques to quantify and explain the differences.
Secondary Subjects:
60K35
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1241702251
Digital Object Identifier: doi:10.1214/08-AAP535
Zentralblatt MATH identifier: 05566101
Mathematical Reviews number (MathSciNet): MR2521889
References
[1] Cranston, M., Mountford, T. S. and Shiga, T. (2002). Lyapunov exponents for the parabolic Anderson model. Acta Math. Univ. Comenian. (N.S.) 71 163–188.
[2] Chow, Y. and Zhang, Y. (2003). Large deviations in first-passage percolation. Ann. Appl. Probab. 13 1601–1614.
[3] Durrett, R. (1995). Ten lectures on particle systems. In Lectures on Probability Theory (Saint-Flour, 1993). Lecture Notes in Math. 1608 97–201. Springer, Berlin.
[4] Deuschel, J.-D. and Zeitouni, O. (1999). On increasing subsequences of I.I.D. samples. Combin. Probab. Comput. 8 247–263.
[5] Grimmett, G. (1999). Percolation, 2nd ed. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 321. Springer, Berlin.
[6] Grimmett, G. and Kesten, H. (1984). First-passage percolation, network flows and electrical resistances. Z. Wahrsch. Verw. Gebiete 66 335–366.
Mathematical Reviews (MathSciNet):
MR751574
[7] Kesten, H. (2003). First-passage percolation. In From Classical to Modern Probability. Progr. Probab. 54 93–143. Birkhäuser, Basel.
[8] Kesten, H. (1986). Aspects of first passage percolation. In École D’été de Probabilités de Saint-Flour, XIV—1984. Lecture Notes in Math. 1180 125–264. Springer, Berlin.
Mathematical Reviews (MathSciNet):
MR876084
[9] Liggett, T. M. (1985). An improved subadditive ergodic theorem. Ann. Probab. 13 1279–1285.
Mathematical Reviews (MathSciNet):
MR806224
[10] Mountford, T. S. (2001). A note on limiting behavior of disastrous environment exponents. Electron. J. Probab. 6 no. 1, 9 pp. (electronic).
[11] Shiga, T. (1997). Exponential decay rate of survival probability in a disastrous random environment. Probab. Theory Related Fields 108 417–439.
