Probabilistic methods are techniques that utilize probability theory to analyze and solve problems, often applied in various fields such as mathematics, statistics, and computer science. These methods are particularly effective in studying systems with inherent randomness and uncertainty, allowing for the derivation of conclusions based on statistical averages rather than deterministic outcomes. In ergodic theory, probabilistic methods help to understand the long-term behavior of dynamical systems by examining the distributions of their trajectories over time.
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