Probability Foundation for Electrical Engineers
Comprehensive exploration of probability theory for electrical engineers, covering fundamental concepts, random variables, expectation, and limit theorems with rigorous mathematical foundations.
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.
A Basic Course in Real Analysis
Explore fundamental concepts of real analysis, including limits, continuity, sets, sequences, series, and theorems. Develop a strong foundation in mathematical reasoning and proof techniques.
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.
On Characterizing Rare Events in Persistent Homology
Explore rare events in persistent homology, focusing on indecomposables in multi-parameter settings. Learn about large deviation principles and laws of large numbers in topological data analysis.
KPZ Limit Theorems
Explores KPZ universality in particle systems, growth models, and polymers, discussing limit theorems, integrable methods, and recent results on periodic domains.
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.
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.
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.
Generalized Law of Iterated Logarithm in the Infinite Horizon Lorentz Gas
Explore the behavior of infinite horizon Lorentz gas, focusing on chaotic dynamics, long flights, and non-standard scaling in limit theorems for billiard particle positions.
Averaging Result for Differential Equations Perturbed by a Z-Periodic Lorentz Gas
Explore averaging results for differential equations perturbed by Z-periodic Lorentz gas, examining asymptotic behavior and convergence rates in infinite measure-preserving systems.
Fluctuation Limits for Mean-Field Interacting Nonlinear Hawkes Processes
Explore fluctuation limits in mean-field interacting nonlinear Hawkes processes, delving into advanced mathematical concepts and their applications.
Lambda-Coalescents Arising in a Population With Dormancy
Explore Lambda-coalescents in populations with dormancy, examining genealogy and multiple ancestral line mergers through a three-season model of spring awakening, summer reproduction, and winter dormancy.