Lectures related to Probabilistic method and its applications

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

Covers graphical models for probability distributions and factor graphs representation.

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Explores graph coloring, directed cycles, LLL algorithm applications, and element dependencies in graphs.

Explores the transition from sparse to dense graphs and their real-world applications.

Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.

Explores Cheeger's inequalities for random walks on graphs and their implications.

Distinguishes between subgraphs and induced subgraphs in graph theory, illustrating the construction of minimal spanning trees.

Covers stochastic properties, network structures, models, statistics, centrality measures, and sampling methods in network data analysis.

Covers the Leighton-Rao algorithm for finding the sparsest cut in a graph, focusing on its steps and theoretical foundations.

Explores the Szemerédi Regularity Lemma, e-regularity in bipartite graphs, supergraph structure, and induction techniques.

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

Covers applied probability, stochastic processes, Markov chains, rejection sampling, and Bayesian inference methods.

Explores Belief Propagation in graphical models, factor graphs, spin glass examples, Boltzmann distributions, and graph coloring properties.

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.

Explains message passing in graphical models and the matching problem in graph theory.

Explores pseudorandomness and the Expander Mixing Lemma in the context of d-regular graphs.

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.