Mini workshop on entropy inequalities for factors of IID
August 22-26, 2016Siófok, 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.
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 measure-conjugacy invariant for free group actions | |
| Ann. Math., 171(2): 1387-1400, 2010. | |
| Lewis Bowen | |
| The ergodic theory of free group actions: entropy and the f-invariant | |
| Groups Geom. Dyn., 4(3):419-432, 2010. | |
| 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. | |
| Mustazee Rahman, Bálint Virág | |
| Local algorithms for independent sets are half-optimal | |
| arXiv:1402.0485, 2014 | |
| Mustazee Rahman | |
| Factor of iid percolation on trees | |
| Theorem 2.2: edge-vertex inequality. | |
| arXiv:1410.3745, 2014 | |
| 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 | |
| Ágnes Backhausz, Balázs Szegedy | |
| On the almost eigenvectors of random regular graphs | |
| arXiv:1607.04785, 2016 | |