Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting "intermittent" behavior that alternates between regular and chaotic patterns. They are characterized by decay of correlations of order 1/n and a central limit theorem with a non-classical scaling factor of √ n log n. As for the growth of the pth moments of the appropriately normalized Birkhoff sums, it follows from the results of [28] that these converge to the moments of the limit normal distribution only for p < 2 and diverge for p > 2. Here we focus on the critical case p = 2 and prove a doubling effect: the second moments converge, but their limit is twice the second moment of the limit normal distribution.
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