Concept

Abelian and Tauberian theorems

Related lectures (31)

Covers hitting probabilities in Markov chains with disjoint subsets, the function h(i), theorems, proofs, and expected time to hit calculations.

Explores the chain rule for compositions of differential functions in higher dimensions, emphasizing gradients and directional changes.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Covers the generalization of the TAF theorem, lateral derivatives, limits of derivatives, and indeterminacy.

Explores the theory of optimal transport, focusing on Lipschitz functions and uniqueness of solutions.

Explores the theorems on maximum and minimum values of functions and their relation to continuity.

Explores the lower bound on total variation distance in Markov chains and its implications on mixing time.

Covers the definition of the center of a function using finite differences and provides step-by-step proofs.

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Covers the basic theory for continuous time Markov chains and discusses communication, hitting probabilities, recurrence, and transience.

Covers the concept of differential operators and presents theorems and proofs related to scalar and vector fields.

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Covers the Triangle Inequality Theorem in triangles, showing side length relationships.

Explores sub/super harmonic functions and their applications in a theoretical context.

Explores recurrence, transience, and invariant distributions in Markov chains with proofs and examples.

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.

Explores continuity, derivability, and linear approximation in mathematical analysis.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Covers the mathematical development of canonical correlation analysis, including population and sample CCA.

Explores the phase diagram of the Ising model, focusing on Gibbs state uniqueness and critical temperatures.