Polymer Models: Basic Observables

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Introduces probability, statistics, distributions, inference, likelihood, and combinatorics for studying random events and network modeling.

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Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Random Walks: Return Probabilities in Lattice Dimensions

Covers random walks on a lattice, focusing on return probabilities and their dependence on dimensionality.

Probability and Statistics: Independence and Conditional Probability

Explores independence and conditional probability in probability and statistics, with examples illustrating the concepts and practical applications.

Conditional Probability: Prediction Decomposition

Explores conditional probability, Bayes' theorem, and prediction decomposition for informed decision-making.

Dependence and Correlation

Explores dependence, correlation, and conditional expectations in probability and statistics, highlighting their significance and limitations.

Introduction to Inference

Covers the basics of probability theory, random variables, joint probability, and inference.

Generalization Error

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Law of Large Numbers: Strong Convergence

Explores the strong convergence of random variables and the normal distribution approximation in probability and statistics.

Probability and Statistics: Fundamentals

Covers the fundamental concepts of probability and statistics, including interesting results, standard model, image processing, probability spaces, and statistical testing.