G. Basile, C. Bernardin, and S. Olla, Momentum Conserving Model with Anomalous Thermal Conductivity in Low Dimensional Systems, Physical Review Letters, vol.96, issue.20, pp.96-204303, 2006.
DOI : 10.1063/1.1561627

G. Basile, C. Bernardin, and S. Olla, Thermal Conductivity for a Momentum Conservative Model, Communications in Mathematical Physics, vol.28, issue.1, pp.67-98, 2009.
DOI : 10.1007/978-3-642-84371-6

URL : http://arxiv.org/pdf/cond-mat/0601544v3.pdf

C. Bernardin, P. Gonçalves, and M. Jara, 3/4-Fractional Superdiffusion in a System of Harmonic Oscillators Perturbed by a Conservative Noise, Archive for Rational Mechanics and Analysis, vol.154, issue.5, pp.505-542, 2016.
DOI : 10.1103/PhysRevLett.108.180601

URL : https://hal.archives-ouvertes.fr/hal-00943116

C. Bernardin, P. Gonçalves, M. Jara, M. Sasada, and M. Simon, From Normal Diffusion to Superdiffusion of Energy in the Evanescent Flip Noise Limit, Journal of Statistical Physics, vol.154, issue.6, pp.1327-1368, 2015.
DOI : 10.1007/s10955-014-0933-y

URL : https://hal.archives-ouvertes.fr/hal-01267034

C. Bernardin and G. Stoltz, Anomalous diffusion for a class of systems with two conserved quantities, Nonlinearity, vol.25, issue.4, pp.1099-1133, 2012.
DOI : 10.1088/0951-7715/25/4/1099

URL : https://hal.archives-ouvertes.fr/ensl-00909792

E. Fermi, J. Pasta, and S. Ulam, Studies of nonlinear problems. I. Los Alamos report LA-1940, published later in Collected Papers, 1955.

P. Gonçalves and M. Jara, Density fluctuations for exclusion processes with long jumps, Probability Theory and Related Fields, vol.4, issue.4, 2015.
DOI : 10.1214/07-PS122

M. Jara, Quadratic Fluctuations of the Simple Exclusion Process, 2014.

M. Jara, T. Komorowski, and S. Olla, Superdiffusion of Energy in a Chain of Harmonic Oscillators with Noise, Communications in Mathematical Physics, vol.154, issue.5, pp.407-453, 2015.
DOI : 10.1007/s10955-014-0933-y

URL : https://hal.archives-ouvertes.fr/hal-00997642

C. Kipnis and C. Landim, Scaling limits of interacting particle systems, 1999.
DOI : 10.1007/978-3-662-03752-2

T. Komorowski, C. Landim, and S. Olla, Time symmetry and martingale approximation, Fluctuations in Markov processes of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00722537

I. Mitoma, Tightness of probabilities on C ([0, 1]; S ) and D([0, Ann. Prob, vol.1, issue.11 4, pp.989-999, 1983.

S. Sethuraman, Central Limit Theorems for Additive Functionals of the Simple Exclusion Process, Ann. Prob, vol.28, pp.277-302, 2000.

W. Whitt, Proofs of the martingale FCLT, Probability Surveys, vol.4, issue.0, pp.268-302, 2007.
DOI : 10.1214/07-PS122