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Lecture
Reversible Chains & Detailed Balance
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Ergodic Theorem: Proof and Applications
Explains the proof of the ergodic theorem and the concept of positive-recurrence in Markov chains.
Markov Chains: Convergence and Spectral Gap
Explores Markov chain convergence, spectral gap, and acceleration techniques for faster convergence.
Mild Dissipative Surface Dynamics
Explores mild dissipative surface dynamics, including conservative behavior and ergodic functions.
Dynamical Approaches to Spectral Theory of Operators
Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.
Joint Equidistribution of CM Points
Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.
Invariant Measures: Properties and Applications
Covers the concept of invariant measures in Markov chains and their role in analyzing irreducible recurrent processes.
Markov Chains: Reversibility and Stationary Distribution
Explores reversibility in Markov chains and its impact on the stationary distribution, highlighting the complexity of non-reversible chains.
Correlations of the Liouville function
Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.
Structure of Measure-Preserving Systems
Covers the abstract structure of measure-preserving systems and aims to understand their classification and ergodic decompositions.
Ergodic properties in exponential dynamics
Explores ergodic properties in exponential dynamics, emphasizing dense orbits and specific functions.