Ergodic Theorem: Basic Tools

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Explores the coupling of Markov chains and the proof of the ergodic theorem, emphasizing distribution convergence and chain properties.

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Covers moments, variance, and expected values in probability and statistics, including the distribution of tokens in a product.

Covers probability theory, distributions, and estimation in statistics, emphasizing accuracy, precision, and resolution of measurements.

Explores the joint equidistribution of CM points and their properties in ergodic theory and homogeneous dynamics.

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Covers probability distributions, moments, and continuous random variables.

Covers basic properties of conditional expectation and Jensen's inequality in probability theory.