On the long time behavior of the stochastic heat equation

Probability Theory and Related Fields

Volumn 114, Issue 3, 1999, Pages 279-289

  Bertini, Lorenzo ^a   Giacomin, Giambattista ^b,c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF ZURICH   (Switzerland)

^c UNIVERSITY OF MILAN   (Italy)

Author keywords

Directed polymers in random environment; Sample Lyapunov exponent; Simple exclusion processes; Stochastic heat equation

Indexed keywords

EID: 0039572010     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050226     Document Type: Article

References (13)

1. Bertini, L., Cancrini, N.: The stochastic heat equation: Feynman-Kac formula and intermittence. J. Stat. Phys., 78, 1377-1401 (1995)
2. Bertini, L., Giacomin, G.: Stochastic Burgers and KPZ equations from particle systems. Comm. Math. Phys., 183, 571-607 (1997)
3. Carmona, R.A., Molchanov, S.A.: Parabolic Anderson model and intermittency. Mem. Amer. Math. Soc. no., 108, (1994)
4. Carmona, R.A., Viens F.G.: Almost-sure exponential behavior of a stochastic Anderson model with continuous space parameter. Stoch. Stoch. Rep. 64, 251-273 (1998)
5. Gärtner, J.: Convergence towards Burgers equation and propagation of chaos for weakly asymmetric exclusion process. Stoch. Processes Appl., 27, 233-260 (1988)
6. Kardar, M.: Replica Bethe ansatz studies of two-dimensional interfaces with quenched random impurities. Nucl. Phys. B, 290, 582-602 (1987)
7. Kardar, M., Parisi, G., Zhang, Y.-C.: Dynamical scaling of growing interfaces. Phys. Rev. Lett., 56, 889-892 (1986)
8. Krug, J., Spohn H.: Kinetic roughening of growing surfaces. In "Solids far from equilibrium: growth, morphology and defects", C. Godrèche ed. Cambridge: Cambridge University Press 1991
9. Liggett, T.M.: Interacting particle systems. Berlin: Springer 1985
10. Molchanov, S.A.: Ideas in the theory of random media. Acta Appl. Math., 22, 139-282 (1991) and references therein
11. Müller, C.: On the support of solutions to the heat equation with noise. Stochastics and Stochastics Reports, 37, 225-245 (1991)
12. Sethuraman, S.: Central limit theorems for additive functionals of symmetric and asymmetric simple exclusion. Preprint, 1997
13. Sethuraman, S., Xu, L.: A central limit theorem for reversible exclusion and zero-range particle systems. Ann. Probab., 24, 1842-1870 (1996)