Long-range algebraic correlations in random matrices induce a transition at H=3/4 in eigenvalue statistics from generalized t-distributions with fat tails to the semicircle law, identified via scaling analysis and simulations.
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In large Lotka-Volterra communities, Gaussian abundance distributions cause feasibility to break before stability, with extinction probabilities governed by a conjectured single-parameter scaling law.
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Long-Range Correlated Random Matrices
Long-range algebraic correlations in random matrices induce a transition at H=3/4 in eigenvalue statistics from generalized t-distributions with fat tails to the semicircle law, identified via scaling analysis and simulations.