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Stretched exponential relaxation ($\exp{-(t/\tau)}^{\beta_K}$) is observed ina large variety of systems but has not been explained so far. Studying randomwalks on percolation clusters in curved spaces whose dimensions range from 2 to7, we show that the relaxation is accurately a stretched exponential and isdirectly connected to the fractal nature of these clusters. Thus we find thatin each dimension the decay exponent $\beta_K$ is related to well-knownexponents of the percolation theory in the corresponding flat space. We suggestthat the stretched exponential behavior observed in many complex systems(polymers, colloids, glasses...) is due to the fractal character of theirconfiguration space.Comment: 5 pages, 3 figures. Submitted to PR

Random walks on fractals and stretched exponential relaxation