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Introduction to Random Walks on Groups

Fields Institute via YouTube

Overview

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Explore the mathematical theory of random walks on groups through this comprehensive graduate-level course from the Fields Institute. Delve into the fundamental concepts, properties, and applications of random processes that evolve on group structures, examining how probability theory intersects with abstract algebra and geometric group theory. Study the behavior of random walks on various types of groups, including finite groups, free groups, and geometric groups, while investigating key topics such as mixing times, spectral properties, and convergence rates. Analyze the relationship between the algebraic structure of groups and the probabilistic behavior of random walks, covering essential techniques for understanding return probabilities, hitting times, and asymptotic behavior. Learn advanced mathematical tools and methods used to study these stochastic processes, including harmonic analysis, representation theory, and geometric techniques. Examine applications to areas such as computer science, statistical mechanics, and geometric group theory through detailed mathematical exposition and rigorous proofs across 21 comprehensive lectures totaling over 6 hours of instruction.

Syllabus

Lecture 01 | Introduction to Random Walks on Groups
Lecture 02 | Introduction to Random Walks on Groups
Lecture 03 | Introduction to Random Walks on Groups
Lecture 04 | Introduction to Random Walks on Groups
Lecture 05 | Introduction to Random Walks on Groups
Lecture 06 | Introduction to Random Walks on Groups
Lecture 07 | Introduction to Random Walks on Groups
Lecture 08 | Introduction to Random Walks on Groups
Lecture 09 | Introduction to Random Walks on Groups
Lecture 10 | Introduction to Random Walks on Groups
Lecture 11 | Introduction to Random Walks on Groups
Lecture 12 | Introduction to Random Walks on Groups
Lecture 13 | Introduction to Random Walks on Groups
Lecture 14 | Introduction to Random Walks on Groups
Lecture 15 | Introduction to Random Walks on Groups
Lecture 16 | Introduction to Random Walks on Groups
Lecture 17 | Introduction to Random Walks on Groups
Lecture 18 | Introduction to Random Walks on Groups
Lecture 19 | Introduction to Random Walks on Groups
Lecture 20 | Introduction to Random Walks on Groups
Lecture 21 | Introduction to Random Walks on Groups

Taught by

Fields Institute

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