Aging for interacting diffusion processes

Dembo, Amir; Deuschel, Jean-Dominique

Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 4, pp. 461-480

[1] G. Ben Arous, Aging and spin-glass dynamics, in: Proceedings of the International Congress of Mathematicians, vol. III, Higher Ed. Press, Beijing, 2002, pp. 3-14. | Zbl | MR

[2] J.P. Bouchaud, L.F. Cugliandolo, J. Kurchan, M. Mezard, Out of equilibrium dynamics in spin-glasses and other glassy systems, in: Young A.P. (Ed.), Spin Glass Dynamics and Random Fields, World Scientific, 1997.

[3] R. Carmona, S.S. Molchanov, Parabolic Anderson problems and intermittency, Mem. Amer. Math. Soc. 108 (1994). | Zbl | MR

[4] L.F. Cugliandolo, Dynamics of glassy systems, in: Lecture Notes in Slow Relaxation and Non Equilibrium Dynamics in Condensed Matter, Les Houches, 2002, Session 77.

[5] L.F. Cugliandolo, J. Kurchan, G. Parisi, Off equilibrium dynamics and aging in unfrustrated systems, J. Phys. I (France) 4 (1994) 1691.

[6] T. Delmotte, Parabolic Harnack inequality and estimates of Markov chains on graphs, Rev. Mat. Iberoamericana 15 (1) (1999) 181-232. | Zbl | MR

[7] J.-D. Deuschel, Algebraic $L_2$-decay of attractive critical processes on the lattice, Ann. Probab. 22 (1994) 264-283. | Zbl | MR

[8] J.-D. Deuschel, The random walk representation for interacting diffusion processes, in: Deuschel J.-D., Greven A. (Eds.), Interacting Stochastic Systems, Springer, Berlin, 2005, pp. 378-391. | Zbl | MR

[9] T. Delmotte, J.-D. Deuschel, On estimating the derivatives of symmetric diffusions in stationary environment with applications to ∇φ interface models, Probab. Theory Related Fields 133 (2005) 358-390. | Zbl

[10] J.-D. Deuschel, T. Nishikawa, The dynamic of entropic repulsion, Stochastic Process. Appl. (2006), in press. | Zbl | MR

[11] J.-D. Deuschel, L. Zambotti, Bismut-Elworthy's formula and random walk representation for SDEs with reflection, Stochastic Process. Appl. 115 (2005) 907-925. | Zbl

[12] J.D. Ferry, Viscoelastic Properties of Polymers, Wiley, New York, 1980.

[13] J. Fröhlich, C.-E. Pfister, On the absence of spontaneous symmetry breaking and of crystalline ordering in two-dimensional systems, Comm. Math. Phys. 81 (1981) 277-298. | MR

[14] T. Funaki, Stochastic interface models, in: Ecole d'été de probabilités de Saint Flour XXXIII - 2003, Lecture Notes in Mathematics, vol. 1869, Springer-Verlag, Berlin, 2005, pp. 105-274. | Zbl

[15] T. Funaki, H. Spohn, Motion by mean curvature from the Ginzburg-Landau ∇φ interface models, Comm. Math. Phys. 185 (1997) 1-36. | Zbl

[16] G. Giacomin, S. Olla, H. Spohn, Equilibrium fluctuations for ∇φ interface model, Ann. Probab. 29 (2001) 1138-1172. | Zbl

[17] A. Greven, Renormalization and universality for multiple population models, in: Deuschel J.-D., Greven A. (Eds.), Interacting Stochastic Systems, Springer, Berlin, 2005, pp. 209-267. | Zbl | MR

[18] B. Helffer, J. Sjöstrand, On the correlation for Kac-like models in the convex case, J. Stat. Phys. 74 (1/2) (1994) 349-409. | Zbl | MR

[19] M. Mezard, G. Parisi, M. Virasoro, Spin Glass Theory and Beyond, World Scientific Lecture Notes in Physics, 1987. | Zbl | MR

[20] C.M. Newman, A general central limit theorem for FKG systems, Comm. Math. Phys. 91 (1983) 75-80. | Zbl | MR

[21] T. Nishikawa, Hydrodynamic limit for the Ginsburg-Landau ∇φ interface model with a conservation law, J. Math. Sci. Univ. Tokyo 9 (2002) 481-519. | Zbl

[22] L.C.E. Struick, Physical Aging in Amorphous Polymers and other Materials, Elsevier, London, 1976.