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We provide a theoretical description of dynamical heterogeneities inglass-forming liquids, based on the premise that relaxation occurs via localrearrangements coupled by elasticity. In our framework, the growth of thedynamical correlation length $\xi$ and of the correlation volume $\chi_4$ arecontrolled by a zero-temperature fixed point. We connect this critical behaviorto the properties of the distribution of local energy barriers at zerotemperature. Our description makes a direct connection between dynamicalheterogeneities and avalanche-type relaxation associated to dynamicfacilitation, allowing us to relate the size distribution of heterogeneities totheir time evolution. Within an avalanche, a local region relaxes multipletimes, the more the larger is the avalanche. This property, related to thenature of the zero-temperature fixed point, directly leads to decoupling ofparticle diffusion and relaxation time (the so-called Stokes-Einsteinviolation). Our most salient predictions are tested and confirmed by numericalsimulations of scalar and tensorial thermal elasto-plastic models.

Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids