Prerequisite chain
Prerequisites for Coupling Arguments and Mixing Time
Topics you need before working through Coupling Arguments and Mixing Time. Direct prerequisites are listed first; transitive prerequisites (the chain reachable through them) follow.
Direct prerequisites (3)
- Metropolis-Hastings Algorithmlayer 2, tier 1
- Martingale Theorylayer 0B, tier 2
- Total Variation Distancelayer 1, tier 1
Reachable through the chain (36)
These topics are not directly cited as prerequisites but are reached transitively by following the chain upward. Working through the direct prerequisites pulls these in.
- Common Probability Distributionslayer 0A, tier 1
- Sets, Functions, and Relationslayer 0A, tier 1
- Basic Logic and Proof Techniqueslayer 0A, tier 2
- Exponential Function Propertieslayer 0A, tier 1
- Integration and Change of Variableslayer 0A, tier 2
- Measure-Theoretic Probabilitylayer 0B, tier 1
- Cardinality and Countabilitylayer 0A, tier 2
- Kolmogorov Probability Axiomslayer 0A, tier 1
- Random Variableslayer 0A, tier 1
- Zermelo-Fraenkel Set Theorylayer 0A, tier 2
- Markov Chain Monte Carlolayer 2, tier 1
- Markov Chains and Steady Statelayer 1, tier 2
- Eigenvalues and Eigenvectorslayer 0A, tier 1
- Matrix Operations and Propertieslayer 0A, tier 1
- Linear Independencelayer 0A, tier 1
- Vectors, Matrices, and Linear Mapslayer 0A, tier 1
- Inner Product Spaces and Orthogonalitylayer 0A, tier 1
- Matrix Normslayer 0A, tier 1
- PageRank Algorithmlayer 2, tier 2
- Graph Algorithms Essentialslayer 0A, tier 2
- Monte Carlo Methodslayer 2, tier 1
- Expectation, Variance, Covariance, and Momentslayer 0A, tier 1
- Joint, Marginal, and Conditional Distributionslayer 0A, tier 1
- Triangular Distributionlayer 0A, tier 2
- Law of Large Numberslayer 0B, tier 1
- Borel-Cantelli Lemmaslayer 0B, tier 1
- Modes of Convergence of Random Variableslayer 0B, tier 1
- Metric Spaces, Convergence, and Completenesslayer 0A, tier 1
- Central Limit Theoremlayer 0B, tier 1
- Characteristic Functionslayer 1, tier 1
- Moment Generating Functionslayer 0A, tier 2
- Stochastic Processes for MLlayer 2, tier 2
- Concentration Inequalitieslayer 1, tier 1
- Common Inequalitieslayer 0A, tier 1
- Radon-Nikodym and Conditional Expectationlayer 0B, tier 1
- Skewness, Kurtosis, and Higher Momentslayer 1, tier 1