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Typicality in random matrix product states

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Quantum Mechanics has been shown to provide a rigorous foundation for Statistical Mechanics. Concentration of measure, or typicality, is the main tool to construct a purely quantum derivation for the methods of Statistical Mechanics. From this point of view statistical ensembles are effective description for isolated quantum systems, since typically a random pure state of the system will have properties similar to those of the ensemble. Nevertheless, it is often argued that most of the states of the Hilbert space are not relevant for realistic systems. This talk will address this issue, presenting recent results on the emergence of typicality in the context of matrix product states, a set of physically and computationally relevant states associated to many-body Hamiltonians.