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Heavy-tailed distributions refer to distributions whose tail probabilities decay slower than exponential speed, such as the Pareto distribution, Student's t distribution, and log-normal distribution; higher-order moments of such distributions may not exist or may diverge, leading to infinite variance.
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10/16/2026
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UnverifiedA heavy-tailed distribution means that the tail of the probability distribution decays much more slowly than that of a normal distribution, meaning that the probability of extreme values occurring is far higher than intuition suggests.80% similarUnverifiedEquilibrium mismatch refers to the learned steady-state distribution itself being far from the target distribution; under certain explicit assumptions, even when the per-atom error in a locally symmetry-preserving model is very small, the distribution discrepancy still approaches its maximum value as the system size increases.76% similarUnverifiedIf a distribution's survival function decays at rate x^{-ν}, it is called a power-law-tailed or heavy-tailed distribution; the smaller ν is, the thicker the tails and the higher the probability of extreme values.76% similarUnverifiedThe smaller the degrees of freedom of the t-distribution, the heavier the tails; as the degrees of freedom approach infinity, the t-distribution converges to the standard normal distribution.73% similarUnverifiedThe ubiquity of the Gaussian distribution stems from the central limit theorem, which states that the sum of a large number of independent random variables tends toward a normal distribution.73% similar
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