The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics. PACS numbers:arXiv:1909.09075v2 [cond-mat.stat-mech]

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Low-temperature quantum phase coherence lengths were experimentally measured in mesoscopic circular arenas fabricated on InGaAs quantum wells. The arenas are connected to wide sample regions by short side-wires, to investigate the effects of geometry in comparison to intrinsic materials properties on quantum decoherence. Universal conductance fluctuations were used to quantify the phase coherence lengths as a function of temperature and geometry. The experimental data show a dependence of phase coherence lengths on side-wire length and width-to-length ratio, which is accounted for by the competing effects of decoherence by coupling to the classical environment and Nyquist decoherence in ergodic wires. The observed decay of phase coherence lengths with the increasing temperature is consistent with expectations. The work demonstrates that geometrical effects influence the measured mesoscopic quantum decoherence.