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Rigorous Scaling Law for the Heat Current in Disordered Harmonic Chain

Bibliographic reference Ajanki, Oskari ; Huveneers, François. Rigorous Scaling Law for the Heat Current in Disordered Harmonic Chain. In: Communications in Mathematical Physics, Vol. 301, no. 3, p. 841-883 (2011)
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  1. Anderson P. W., Absence of Diffusion in Certain Random Lattices, 10.1103/physrev.109.1492
  2. Arnold Ludwig, Random Dynamical Systems, ISBN:9783642083556, 10.1007/978-3-662-12878-7
  3. Azuma Kazuoki, Weighted sums of certain dependent random variables, 10.2748/tmj/1178243286
  4. Bonetto, F., Lebowitz, J.L., Rey-Bellet, L.: Fourier’s law: a challenge to theorists. In: Mathematical physics 2000. London: Imp. Coll. Press, 2000, pp. 128–150
  5. Carlen E.A., Kusuoka S., Stroock D.W.: Upper bounds for symmetric Markov transition functions. Ann. Inst. H. Poincaré, section B 23(2 suppl.), 245–287 (1987)
  6. Casher A., Lebowitz J. L., Heat Flow in Regular and Disordered Harmonic Chains, 10.1063/1.1665794
  7. Coulhon T., Saloff-Coste L.: Puissances d’un opérateur régularisant. Ann. Inst. H. Poincaré, section B 26(3), 419–436 (1990)
  8. Coulhon Th., Saloff-Coste L., Minorations pour les cha�nes de Markov unidimensionnelles, 10.1007/bf01195074
  9. Dhar Abhishek, Heat Conduction in the Disordered Harmonic Chain Revisited, 10.1103/physrevlett.86.5882
  10. Dhar Abhishek, Heat transport in low-dimensional systems, 10.1080/00018730802538522
  11. Diaconis P., Saloff-Coste L., Nash inequalities for finite Markov chains, 10.1007/bf02214660
  12. Escauriaza Luis, Bounds for the fundamental solutions of elliptic and parabolic equations : In memory of eugene fabes, 10.1080/03605300008821533
  13. Freedman David A., On Tail Probabilities for Martingales, 10.1214/aop/1176996452
  14. Guivarc’h, Y.: Limit Theorems for Random Walks and Products of Random Matrices. In: CIMPA-TIFR School on Probability Measures on Groups: Recent Directions and Trends (Mumbai) 2002, New Delhi Natosa pub., 2006
  15. Hall P., Heyde C.C.: Martingale limit theory and its application. Academic Press, London-New York (1980)
  16. Lepri, S., Livi, R., Politi, A.: Anomalous heat conduction. In: Anomalous Transport: Foundations and Applications, Klages, R., Radons, G., Sokolov, I.M. (eds.), Weinheim: Wiley-VCH Verlag, 2008, Ch. 10
  17. Matsuda Hirotsugu, Ishii Kazushige, Localization of Normal Modes and Energy Transport in the Disordered Harmonic Chain, 10.1143/ptps.45.56
  18. Mustapha Sami, Gaussian estimates for spatially inhomogeneous random walks on Z d, 10.1214/009117905000000440
  19. O'Connor A. J., A central limit theorem for the disordered harmonic chain, 10.1007/bf01609867
  20. Peierls R., Zur kinetischen Theorie der Wärmeleitung in Kristallen, 10.1002/andp.19293950803
  21. Peierls R.E.: Quantum Theory of Solids. Oxford University Press, London (1955)
  22. Raugi, A.: Théorème ergodique multiplicatif. Produits de matrices aléatoires indépendantes (Rennes, 1997), Rennes: Publ. Inst. Rech. Math. Rennes, 1997, pp. 1–43
  23. Rieder Z., Lebowitz J. L., Lieb E., Properties of a Harmonic Crystal in a Stationary Nonequilibrium State, 10.1063/1.1705319
  24. Rubin Robert J., Greer William L., Abnormal Lattice Thermal Conductivity of a One‐Dimensional, Harmonic, Isotopically Disordered Crystal, 10.1063/1.1665793
  25. Verheggen Theo, Transmission coefficient and heat conduction of a harmonic chain with random masses: Asymptotic estimates on products of random matrices, 10.1007/bf01562542