Related lectures (35)
Independence and Products
Covers independence between random variables and product measures in probability theory.
Percolation Theory: FKG Inequality
Explores the FKG inequality in percolation theory and the reverse FKG theorem.
Measure Spaces: Integration and Inequalities
Covers measure spaces, integration, Radon-Nikodym property, and inequalities like Jensen, Hölder, and Minkowski.
Differential Forms Integration
Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.
Invariant Measures: Properties and Applications
Covers the concept of invariant measures in Markov chains and their role in analyzing irreducible recurrent processes.
Introduction and Notations
Introduces advanced probability concepts, focusing on key notations and conventions.
Expectation of a Random Variable
Defines the expectation for random variables, emphasizing the importance of absolute values.
Social Network Analysis: Modularity Measure
Explores the computation of the modularity measure and betweenness centrality in graphs for community detection.
Preliminaries in Measure Theory
Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.
Girsanov: Martingales and Brownian Motion
Explores martingales, Brownian motion, and measure transformations in probability theory.

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