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Welcome the web page of the course Stationary Dynamics, given at BGU by Yair Hartman.
Some reading material:
Furman's survey paper (Chapter 2)
Bader-Shalom (Preliminaries section)
An Introduction to Poisson Boundaries of Lie Groups by Babilot
My old lecture notes
Below you'll find the calendar with links to the zoom meetings.
Lecture 1 - 28/02
Lecture 1 - 28/02
General overview and some application of the Furstenberg-Poisson boundary theory.
Standard Borel spaces.
Links: Zoom recording, Jamboard
Lecture 2 - 2/03
Lecture 2 - 2/03
Standard probability spaces and their factors.
Links: Zoom recording, Jamboard
Lecture 3 - 7/03
Lecture 3 - 7/03
Measure class preserving, probability measure preserving
Ergodicity
Links: Zoom recording, Jamboard
Lecture 5 - 14/03
Lecture 5 - 14/03
Random walks on groups - examples
Stationary measures - part 1
Links: Zoom recording Jamboard
Lecture 6 - 16/03
Lecture 6 - 16/03
Stationary measures - part 2
Kakutani's ergodic theorem - part 1
Links: Zoom recording Jamboard
Lecture 7 - 21/03
Lecture 7 - 21/03
Martingale convergence theorem
Bounded harmonic functions
Links: Zoom recording Jamboard
Lecture 8 - 04/04
Lecture 8 - 04/04
Choquet-Deny theorem
Conditional measures
Links: Zoom recording Jamboard
Lecture 9 - 06/04
Lecture 9 - 06/04
Stationary Joining
Boundary Theory
Links: Zoom recording Jamboard
Lecture 10 - 11/04
Lecture 10 - 11/04
The Furstenbeg-Poisson Boundary (part 1)
Links: Zoom recording Jamboard
Lecture 11 - 13/04
Lecture 11 - 13/04
The Furstenbeg-Poisson Boundary (part 2)
Links: (partial) Zoom recording Jamboard
Lecture 22 - 30/05
Lecture 22 - 30/05
Amenability (Thanks to Dor!)
Links: Zoom recording Notes - To be added
Lecture 12 - 18/04
Lecture 12 - 18/04
The Furstenbeg-Poisson Boundary (part 3 - as shift ergodic componenets)
Links: Zoom recording Jamboard
Lecture 13 - 21/04
Lecture 13 - 21/04
Hyperbolic groups - thanks to Anna!
Links: Zoom recording Jamboard
Lecture 14 - 25/04
Lecture 14 - 25/04
Hyperbolic groups (cont.)
Examples of boundaries
Links: Zoom recording Jamboard
Lecture 15 - 27/04
Lecture 15 - 27/04
Abstract definition of boundaries
Links: Zoom recording Jamboard
Lecture 16 - 02/05
Lecture 16 - 02/05
Endomorphisms of mu-boundaries
Furstenberg-Poisson boundary of quotient groups
Links: Zoom recording Jamboard
Lecture 17 - 04/05
Lecture 17 - 04/05
SAT vs. mu-boundaries - thanks to Jonathan!
Links: Zoom recording Jamboard
Lecture 18 - 09/05
Lecture 18 - 09/05
Shannon entropy (thanks to Amit!)
Links: Zoom recording Notability, see also this for more details
Lecture 19 - 11/05
Lecture 19 - 11/05
Furstenberg entropy
Links: Zoom recording Jamboard
Lecture 20 - 19/05
Lecture 20 - 19/05
Subexponential groups
Recurrent subgroup
Links: Zoom recording Jamboard
Lecture 21 - 23/05
Lecture 21 - 23/05
Relative measure-preserving factors
Links: Zoom recording Jamboard
Lecture 22 - 30/05
Lecture 22 - 30/05
Amenability (Thanks to Dor!)
Links: Zoom recording Notes
Lecture 23 - 6/06
Lecture 23 - 6/06
Property (T)
Some preparations for the Normal Subgroup Theorem
Links: Zoom recording Jamboard
Lecture 24 - 8/06
Lecture 24 - 8/06
From Factor Theorem to Normal Subgroup Theorem
Links: Zoom recording Jamboard
Lecture 25 - 13/06
Lecture 25 - 13/06
C*-algebras, Gelfand Spectrum, and GNS (Thanks to Yeari!)
Links: Zoome recording part 1, part 2, Yeari's extended notes
Lecture 26 - 15/06
Lecture 26 - 15/06
Invariant Random Subgroups and Schreier graph (Thanks to Omer!)
Links: Zoom recording, Omer's notes, Jamboard with some photographic subgroups
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