Mini workshop on entropy inequalities for factors of IID
August 2226, 2016 Siófok, Hungary
Topics and goals
Entropy inequalities proved to be a key tool
in a couple of remarkable results recently:
the RahmanVirág result about the maximal size of a factor of IID
independent set on the regular tree and
the BackhauszSzegedy result on eigenvectors of random regular graphs.
The main focus of this mini workshop will be to investigate these inequalities,
look for further applications, and try to obtain new inequalities as well.
Another goal of the workshop is to study a series of papers by Lewis Bowen
in which he introduced the finvariant for free group actions
and the soficentropy for actions of sofic groups.
Bowen also showed that the finvariant is essentially a special case
of the the soficentropy which has the consequence that
the finvariant is nonnegative for factors of the Bernoulli shift.
This fact is particularly relevant for us
since it is equivalent to (a somewhat more general version of)
the edgevertex entropy inequality for factors over the free group.
Registration
Organizer: Viktor Harangi (Rényi Institute)
If you are interested in participating in the workshop, please write me at
Confirmed participants
Backhausz, Ágnes
Csóka, Endre (?)
Gerencsér, Balázs
Harangi, Viktor
Vizer, Máté
Relevant literature
Lewis Bowen

A measureconjugacy invariant for free group actions

Ann. Math., 171(2): 13871400, 2010. 
pdf

Lewis Bowen

The ergodic theory of free group actions: entropy and the finvariant

Groups Geom. Dyn., 4(3):419432, 2010. 
pdf

Lewis Bowen

Nonabelian free group actions: Markov processes,
the AbramovRohlin formula and Yuzvinskii’s formula

Section 9: finvariant for Markov chains over free groups.

Ergod. Th. & Dynam. Sys. 30, no. 6, 16291663, 2010. 
pdf

Mustazee Rahman, Bálint Virág

Local algorithms for independent sets are halfoptimal

arXiv:1402.0485, 2014 
pdf

Mustazee Rahman

Factor of iid percolation on trees

Theorem 2.2: edgevertex inequality.

arXiv:1410.3745, 2014 
pdf

Ágnes Backhausz, Balázs Szegedy

On large girth regular graphs and random processes on trees

Theorem 3: edgevertex inequality. Theorem 4: staredge inequality.

arXiv:1406.4420, 2014 
pdf

Ágnes Backhausz, Balázs Szegedy

On the almost eigenvectors of random regular graphs

arXiv:1607.04785, 2016 
pdf

