Convergence Rate Theorem: Part 2

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Page 2 of 4

Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.

Covers the concepts of contraposition and contradiction in proofs.

Discusses the sharp transition in mixing time of a random walk.

Explores transience and recurrence in Markov chains, emphasizing birth and death chains and random walks.

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

Explores the lower bound on total variation distance in Markov chains and its implications on mixing time.

Introduces the basics of automata theory and explores the theorems of regular languages.

Explores Boolean algebra, optimization, sequential systems, and finite state machines design.

Covers the conversion from finite automata to regular expressions and exercises on constructing deterministic finite automata.

Illustrates ergodicism in continuous-time stochastic processes through examples and calculations.