Limit theorems Courses and Certifications

Probability - The Science of Uncertainty and Data

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Build foundational knowledge of data science with this introduction to probabilistic models, including random processes and the basic elements of statistical inference -- Part of the MITx MicroMasters program in Statistics and Data Science.

• edX
• 16 weeks, 10-14 hours a week
• On-Demand
• Free Online Course (Audit)

• Best of All Time

Hausdorff Center for Mathematics

Limit Theorems for the Volumes of Small Codimensional Random Sections of Lpn-Balls

Explore central limit theorems for volumes of random sections in high-dimensional geometry, with insights on open questions and recent research developments.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Takashi Owada - Limit Theorems for Topological Invariants of the Dynamic Multi-Parameter Simplicial Complex

Explore topological invariants in dynamic multi-parameter simplicial complexes, covering connectivity, probability, and limiting processes in applied algebraic topology.

• YouTube
• 28 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Limit Theorems in Topological Data Analysis

Explore limit theorems in topological data analysis, focusing on barcodes, persistence modules, and random persistence modules. Learn about convergence proofs and expectations for uniform distributions on compact submanifolds.

• YouTube
• 58 minutes
• On-Demand
• Free Video

International Mathematical Union

KPZ Limit Theorems

Explores KPZ universality in particle systems, growth models, and polymers, discussing limit theorems, integrable methods, and recent results on periodic domains.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Counting Limit Theorems for Representations of Gromov-Hyperbolic Groups

Explore limit theorems for Gromov-hyperbolic group representations, examining statistical results analogous to random matrix products theory for spherical averages in the S-metric.

• YouTube
• 39 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Limit Theorems in Finite Free Probability

Explore recent limit theorems in finite free probability, including techniques, implications, connections to empirical measure convergence of polynomial roots, and a new variational characterization of free convolutions.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Limit Theorems for Lacunary Sequences and Discrepancy

Explore the probabilistic analysis of trigonometric sums with Hadamard gap conditions, including limit theorems, asymptotic expansions, and sublacunary sequences using Diophantine analysis methods.

• YouTube
• 55 minutes
• On-Demand
• Free Video

statisticsmatt

Basic Limit Theorems

Explore fundamental limit theorems in probability and statistics, including convergence modes, central limit theorem, and law of large numbers, with practical examples and proofs.

• YouTube
• 3 hours 30 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Andrew Thomas - Functional Limit Theorems for Euler Characteristic Processes

Explore functional limit theorems for Euler characteristic processes in Vietoris-Rips complexes, covering strong law of large numbers and central limit theorem in the thermodynamic regime.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Poisson Limit Theorems for Systems with Product Structure

Explore Poisson Limit Theorems for product systems, focusing on return times to small sets and applications to various map combinations, including Anosov and skew products.

• YouTube
• 34 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Combinatorial Identities for Partition Sets and Limit Theorems in Free Probability

Explore combinatorial identities for partition sets and their connections to limit theorems, finite free convolutions, and asymptotic behavior of Unitary Hermite and Laguerre Polynomials.

• YouTube
• 41 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Central Limit Theorems for Poisson Functionals - The Malliavin-Stein Approach

Explore central limit theorems in stochastic geometry using the Malliavin-Stein method, with applications to random point collections and the Online Nearest Neighbour Graph.

• YouTube
• 25 minutes
• On-Demand
• Free Video

Fields Institute

A Survey of Central Limit Theorems in Number Theory

Explore key central limit theorems in number theory, examining their applications and implications for understanding mathematical distributions and patterns.

• YouTube
• 36 minutes
• On-Demand
• Free Video

ICTP-SAIFR

Classical Limit of the Higher-Order Soft Graviton Theorems in D=4

Explore the classical limit of higher-order soft graviton theorems in four-dimensional spacetime through advanced theoretical physics analysis.

• YouTube
• 22 minutes
• On-Demand
• Free Video