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Analysis of a stochastic branching recursion related to the Anderson transition

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One way to describe the Anderson transition is that eigenvectors of a large random Hermitian matrix undergo a transition from extended (macroscopic number on non-zero entries) to localized (only finitely many non-zero entries) as one “strengthens the randomness” in the matrix. Physicists believe that precisely at the transition point, the eigenvectors should exhibit multi-fractal behaviour (anomalous scaling). We will consider a specific random matrix model and study its multifractal behaviour through a heuristic approximation resulting in a stochastic branching recursion similar to those appearing in the study of multiplicative cascades.

This talk is part of the Probability series.

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