Math 996: Topics in Probability
In this course we aim to cover several core topics leading to a proof of the Ornstein isomorphism theorem:
1.) The ergodic theorem.
2.) Kolmogorov-Sinai entropy.
3.) Shannon-McMillan-Breiman theorem.
4.) The isomorphism problem.
5.) The Ornstein isomorphism theorem.
No textbook is required.
Grading: homework and presentations.
Prerequisites: working knowledge of measure theory, good background in probability and analysis.
LEC Topic: Topics in Probability Soo, Terry 3 22386 (Save) 15
Notes TR 02:30 -03:45 PM SNOW 456 - LAWRENCE
Paul Shields, The theory of Bernoulli shift:
Karl Petersen, Ergodic theory:
Downarowicz and Searfin, A short proof of the Ornstein theorem:
Keane and Smorodinksy, Bernoulli schemes of the same entropy are finitarily isomorphic
Some Lecture notes