Second part of the talk from last week:

An ergodic system (X;B; μ; T) is said to have the weak Pinsker

property if for any ε > 0 one can express the system as the direct

product of two systems with the first having entropy less than ε and

the second one being isomorphic to a Bernoulli system. The problem

as to whether or not this property holds for all systems was open for

more than forty years and has been recently settled in the affirmative

in a remarkable work by Tim Austin.

I will begin by describing why Jean-Paul formulated this prob-

lem and its significance. Then I will give an aerial view of Tim's

proof. His main new contribution is a general result on the struc-

ture of probability distributions of nite sequences of random vari-

ables {X1,X2,...,Xn}. All of concepts involved will be defined from

scratch.

An ergodic system (X;B; μ; T) is said to have the weak Pinsker

property if for any ε > 0 one can express the system as the direct

product of two systems with the first having entropy less than ε and

the second one being isomorphic to a Bernoulli system. The problem

as to whether or not this property holds for all systems was open for

more than forty years and has been recently settled in the affirmative

in a remarkable work by Tim Austin.

I will begin by describing why Jean-Paul formulated this prob-

lem and its significance. Then I will give an aerial view of Tim's

proof. His main new contribution is a general result on the struc-

ture of probability distributions of nite sequences of random vari-

ables {X1,X2,...,Xn}. All of concepts involved will be defined from

scratch.

## Date:

Thu, 17/05/2018 - 16:00 to 17:30

## Location:

Ross 70