A minimal neighbor-interaction Lotka-Volterra model yields exponentially many self-organized species cluster states separated by sharp phase transitions, exactly solvable via transfer matrices in the nearest-neighbor limit.
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Pedagogical lecture notes derive standard RMT laws with the cavity method, illustrate applications, and catalogue advanced analytical techniques for disordered systems.
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Minimal model of self-organized clusters with phase transitions in ecological communities
A minimal neighbor-interaction Lotka-Volterra model yields exponentially many self-organized species cluster states separated by sharp phase transitions, exactly solvable via transfer matrices in the nearest-neighbor limit.
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Lecture notes on random matrix theory: the results, the applications, and the analytical tools
Pedagogical lecture notes derive standard RMT laws with the cavity method, illustrate applications, and catalogue advanced analytical techniques for disordered systems.