Below a critical entropy H_c ≈ log K - 1 + γ in the large-K limit, the typical fixed-entropy distribution on the probability simplex condenses so that one component holds a macroscopic probability fraction while the rest form a uniform background.
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Condensation Transition in Entropy-Constrained Probability Spaces
Below a critical entropy H_c ≈ log K - 1 + γ in the large-K limit, the typical fixed-entropy distribution on the probability simplex condenses so that one component holds a macroscopic probability fraction while the rest form a uniform background.