Fig. 6.

Ripple Events’ stochasticity. (A) A histogram of intervals between RE is nearly exponential. (B) The averages ⟨λ_re⟩ and ⟨β_re⟩ are high, indicating both frequent deviation of RE from the mean and higher temporal clustering than for the θ- and γ-patterns. (C) The animal’s speed (gray line, Top panel) correlates with the Kolmogorov parameter λ_re during fast exploratory laps. During inactivity (vertical gray stripes), the λ_re-stochasticity uncouples from speed, exhibiting high spikes that mark strong “fibrillation” of RE patterns and may reflect awake replay activity. The antiphasic relationship between the animal’s acceleration a(t) (gray line, Bottom panel) and Arnold score β_re(t) shows that RE tends to cluster when as the animal decelerates, while acceleration enforces periodicity. During slower moves (gray stripes), the relationship between speed, acceleration, and stochasticity is washed out and stochastically improbable patterns dominate. (D) Locally averaged ${\widehat{\lambda }}_{\mathit{re}}$ grows with speed and ${\widehat{\beta }}_{\mathit{re}}$ drops with acceleration.