Lectures related to Probability Theory: Markov's Theorem

Covers probabilistic methods in combinatorics, monochromatic edges, 2-colorable graphs, and good 2-colorings.

Explores the theory of martingales, including conditional expectations, Chernoff bounds, and Azuma's inequality.

Covers the Poisson Paradigm, including the First/Second Moment Method and Martingales, discussing dependency graphs and Chernoff bounds.

Explores the Poisson Paradigm and dependency measures in ordered pairs and graphs.

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

Covers topics related to probability and statistics, including finding specific values and significant events.

Covers girth, independence, probability, union bound, sets, and hypergraph recoloring.

Explores Brun's Sieve, Martingales, and Conditional Expectations in probability theory.

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Explores the FKG inequality in percolation theory and the reverse FKG theorem.

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

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

Introduces key concepts in probability and statistics, such as events, Venn diagrams, and conditional probability.

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

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

Focuses on open problems and the importance of reformulating problems with better tools and intuition.

Explores variance, covariance, and practical applications in statistics and probability.

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