Mini workshop on entropy inequalities for factors of IID

August 22-26, 2016
Siófok, Hungary

Topics and goals

Entropy inequalities proved to be a key tool in a couple of remarkable results recently: the Rahman-Virág result about the maximal size of a factor of IID independent set on the regular tree and the Backhausz-Szegedy 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 f-invariant for free group actions and the sofic-entropy for actions of sofic groups. Bowen also showed that the f-invariant is essentially a special case of the the sofic-entropy which has the consequence that the f-invariant is non-negative 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 edge-vertex entropy inequality for factors over the free group.


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 measure-conjugacy invariant for free group actions
Ann. Math., 171(2): 1387-1400, 2010. pdf

Lewis Bowen
The ergodic theory of free group actions: entropy and the f-invariant
Groups Geom. Dyn., 4(3):419-432, 2010. pdf

Lewis Bowen
Nonabelian free group actions: Markov processes, the Abramov-Rohlin formula and Yuzvinskii’s formula
Section 9: f-invariant for Markov chains over free groups.
Ergod. Th. & Dynam. Sys. 30, no. 6, 1629-1663, 2010. pdf

Mustazee Rahman, Bálint Virág
Local algorithms for independent sets are half-optimal
arXiv:1402.0485, 2014 pdf

Mustazee Rahman
Factor of iid percolation on trees
Theorem 2.2: edge-vertex inequality.
arXiv:1410.3745, 2014 pdf

Ágnes Backhausz, Balázs Szegedy
On large girth regular graphs and random processes on trees
Theorem 3: edge-vertex inequality. Theorem 4: star-edge inequality.
arXiv:1406.4420, 2014 pdf

Ágnes Backhausz, Balázs Szegedy
On the almost eigenvectors of random regular graphs
arXiv:1607.04785, 2016 pdf