Stochastic Processes: Ergodicity

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Stochastic Processes: Ergodicity

Covers the concept of ergodicity in continuous-time stochastic processes.

Theory of MCMC

Covers the theory of Markov Chain Monte Carlo (MCMC) sampling and discusses convergence conditions, transition matrix choice, and target distribution evolution.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Statistical Physics: Systems Isolation

Explores statistical physics concepts in isolated systems, focusing on entropy and disorder.

Vectors of Random Variables: Empirical Distributions

Discusses vectors of random variables and empirical distributions, including their properties and significance in statistics.

Signals & Systems II: Second Order Statistics

Explores second order statistics in signal processing, stationarity in random signals, and the distinction between ergodic and non-ergodic processes.

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Probabilistic Functions: Free Fields and Random Variables

Covers free fields and probabilistic functions, focusing on random variables and their properties.

Joint Equidistribution of CM Points

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

Markov Chains: Reversibility & Convergence

Covers Markov chains, focusing on reversibility, convergence, ergodicity, and applications.