Math 996: Topics in Probability

Terry Soo

 

 

In this course we aim to cover several core topics leading to a proof of the Ornstein isomorphism theorem:

 

Wikipedia entry

 

For example:

 

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.


Possible presentation topics
 

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   

 

References:

 

Paul Shields, The theory of Bernoulli shift:

Link

 

Karl Petersen, Ergodic theory:

Amazon link

 

Downarowicz and Searfin,  A short proof of the Ornstein theorem:

Journal link

 

Keane and Smorodinksy, Bernoulli schemes of the same entropy are finitarily isomorphic

Jounral link

 

 

Some Lecture notes

 

lec1-intro.pdf

 

lec2-von.pdf


lec3-entropy.pdf


lec4-entropycond.pdf


lec5-shannon.pdf


lec6-birk.pdf


lec7-large.pdf


lec8-smb.pdf


lec9-rohklin.pdf


lec10-orn.pdf


lec11-joining.pdf


lec12-sketch.pdf