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Signatures of critical full counting statistics in a quantum-dot chain

We consider current shot noise and the full counting statistics in a chain of quantum dots which exhibits a continuous non-equilibrium phase transition as a function of the tunnel couplings of the chain with the electrodes. Using a combination of analytical and numerical methods, we establish that the full counting statistics is conventional away from the phase transition, but becomes, in a well-defined sense, essentially non-Gaussian on the critical line, where the current fluctuations are controlled by the dynamic critical exponent $z$. We find that signatures of the critical full counting statistics persist in quantum-dot chains of finite length.