Random Schrödinger operators arising in the studyof reinforced random processes

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In recent years, reinforced random processes have attracted much interest from the scientific community due to the discovery of connections with different areas of mathematics that have allowed for rigorous proofs of phase transitions in these models. In this proposal, we are interested in a recently discovered connection with certain random Schrödinger operators, which are used to model the propagation of electrons in disordered media. Our goal is to combine the well developed theory of quantum disordered systems with these new results and exploit these connections further to study phase transitions in disordered quantum systems. We expect our work to provide at least a partial answer to a recent question formulated by Sabot and Zeng, and with this, to contribute to the understanding of a long-standing open problem in the theory of disordered solids, namely, the Anderson metal-insulator transition for disordered quantum systems.