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We study in details the dynamics of the one dimensional symmetric trap model,via a real-space renormalization procedure which becomes exact in the limit ofzero temperature. In this limit, the diffusion front in each sample consists intwo delta peaks, which are completely out of equilibrium with each other. Thestatistics of the positions and weights of these delta peaks over the samplesallows to obtain explicit results for all observables in the limit $T \to 0$.We first compute disorder averages of one-time observables, such as thediffusion front, the thermal width, the localization parameters, thetwo-particle correlation function, and the generating function of thermalcumulants of the position. We then study aging and sub-aging effects : ourapproach reproduces very simply the two different aging exponents and yieldsexplicit forms for scaling functions of the various two-time correlations. Wealso extend the RSRG method to include systematic corrections to the previouszero temperature procedure via a series expansion in $T$. We then consider thegeneralized trap model with parameter $\alpha \in [0,1]$ and obtain that thelarge scale effective model at low temperature does not depend on $\alpha$ inany dimension, so that the only observables sensitive to $\alpha$ are thosethat measure the `local persistence', such as the probability to remain exactlyin the same trap during a time interval. Finally, we extend our approach at ascaling level for the trap model in $d=2$ and obtain the two relevant timescales for aging properties.Comment: 33 pages, 3 eps figure

Anomalous diffusion, localization, aging, and subaging effects in trap models at very low temperature