Probabilistic method and its applications

Related lectures (35)

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.

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.

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

Covers the basics of graph theory, including network flows, degrees of vertices, walks, and subgraphs.

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

Covers the basics of the Lovász Local Lemma, including mutually independent bad events and pseudoprobabilities.

Explores optimization techniques, word embeddings, and recommendation systems in machine learning.

Covers differential operators, vector analysis, Fourier analysis, and potential fields with applications to gravity.

Explores channel coding, BICM, and LLRs in wireless communication systems, emphasizing the importance of error detection and correction.

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