Lectures related to Convergence Rate Theorem: Part 2

Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Explains the proof of the ergodic theorem and the concept of positive-recurrence in Markov chains.

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

Introduces the basics of finite automata, including deterministic and non-deterministic types, regular expressions, and acceptance criteria.

Covers the fundamentals of regular expressions and includes exercises on defining languages.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Introduces finite state machines, covering basics, design, and practical applications like decoders and encoders.

Covers examples of direct and indirect proofs in mathematics.

Explores the transition from regular expressions to finite automata, covering lexer creation, different automata types, and conversion processes.

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.