Superdiffusivity of the 1D lattice Kardar-Parisi-Zhang equation

Journal of Statistical Physics

Volumn 137, Issue 5, 2009, Pages 917-935

  Sasamoto, Tomohiro ^a   Spohn, Herbert ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Continuum growth model; Non hermitian bosonic field theory

Indexed keywords

EID: 74449092936     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-009-9831-0     Document Type: Article

References (22)

1. Johansson, K.: Random matrices and determinantal processes. In: Bovier, A., et al. (eds.) Math. Stat. Phys., Session LXXXIII: Lecture Notes of the Les Houches Summer School 2005, pp. 1-56. Elsevier Science, Amsterdam (2006).
2. Spohn, H.: Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals. Physica A 369, 71-99 (2006).
3. Sasamoto, T.: Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques. J. Stat. Mech. P07007 (2007).
4. Prähofer, M., Spohn, H.: Exact scaling function for one-dimensional stationary KPZ growth. J. Stat. Phys. 115, 255-279 (2004).
5. Ferrari, P. L., Spohn, H.: Scaling limit for the space-time covariance of the stationary totally asymmetric simple exclusion process. Commun. Math. Phys. 265, 1-44 (2006).
6. Kardar, M., Parisi, G., Zhang, Y. Z.: Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889-892 (1986).
7. Katzav, E., Schwartz, M.: Numerical evidence for stretched exponential relaxations in the Kardar-Parisi-Zhang equation. Phys. Rev. E 69, 052603 (2004).
8. Bertini, L., Giacomin, G.: Stochastic Burgers and KPZ equations from particle systems. Commun. Math. Phys. 183, 571-607 (1997).
9. Balazs, M., Quastel, J., Seppalainen, T.: Scaling exponent for the Cole-Hopf solution of KPZ/stochastic Burgers. arXiv: 0909. 4816.
10. Bernardin, C.: Superdiffusivity of asymmetric energy model in dimension one and two. J. Math. Phys. 49, 103301 (2008).
11. Miyao, T.: Private communication (2009).
12. Gotoh, T., Kraichnan, R. H.: Burgers turbulence with large scale forcing. Phys. Fluids A 10, 2859-2866 (1998).
13. E, W., Khanin, K., Mazel, A., Sinai, Y.: Invariant measures for Burgers equation with stochastic forcing. Ann. Math. 151, 877-960 (2000).
14. Krug, J., Spohn, H.: Kinetic roughening of growing surfaces. In: Godrèche, C. (ed.) Solids Far from Equilibrium, pp. 412-525. Cambridge University Press, Cambridge (1991).
15. Lam, C.-H., Shin, F. G.: Improved discretization of the Kardar-Parisi-Zhang equation. Phys. Rev. E 58, 5592-5595 (1998).
16. Schweber, S.: An Introduction to Relativistic Quantum Field Theory. Harper & Row, New York (1966).
17. Landim, C., Quastel, J., Salmhofer, M., Yau, H.-T.: Superdiffusivity of asymmetric exclusion process in dimensions one and two. Commun. Math. Phys. 244, 455-481 (2004).
18. Baik, J., Ferrari, P., Péché, S.: Limit process for the TASEP near a characteristic line. arXiv: 0907. 0226.
19. Ziman, J. M.: Electrons and Phonons: The Theory of Transport Phenomena in Solids. Oxford University Press, New York (1987).
20. Frachebourg, I., Martin, Ph. A.: Exact statistical properties of the Burgers equation. J. Fluid Mech. 417, 323-349 (2000).
21. Chabanol, M.-L., Duchon, J.: Markovian solutions of inviscid Burgers equation. J. Stat. Phys. 114, 525-534 (2004).
22. Burgers, J. M.: The Nonlinear Diffusion Equation. Reidel, Dordrecht (1974).