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Entropy and mixing for multidimensional shifts of finite type - Lecture 1
Post-edited
Authors : Pavlov, Ronnie (Author of the conference)
CIRM (Publisher )
37B10 - Symbolic dynamics
37B40 - Topological entropy
37B50 - Multi-dimensional shifts of finite type, tiling dynamics
CIRM (Publisher )
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| symbolic system $Z^d$ shifts of finite type topological entropy computability strong irreducibility measures measure-theoretic entropy measure of maximal entropy Markov measure |
Abstract :
I will speak about multidimensional shifts of finite type and their measures of maximal entropy. In particular, I will present results about computability of topological entropy for SFTs and measure-theoretic entropy. I'll focus on various mixing hypotheses, both topological and measure-theoretic, which imply different rates of computability for these objects, and give applications to various systems, including the hard square model, k-coloring, and iceberg model.
MSC Codes : 37B10 - Symbolic dynamics
37B40 - Topological entropy
37B50 - Multi-dimensional shifts of finite type, tiling dynamics
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 09/02/2017 Conference Date : 31/01/17 Subseries : Research School arXiv category : Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE Format : MP4 (.mp4) - HD Video Time : 01:00:49 Targeted Audience : Researchers ; Graduate Students Download : https://videos.cirm-math.fr/2017-01-31_Pavlov_part1.mp4 
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Information on the Event
Event Title : New advances in symbolic dynamics / Dynamique symbolique, Combinatoire des mots. Calculabilité. AutomatesEvent Organizers : Durand, Fabien ; Frid, Anna ; Sablik, Mathieu Dates : 30/01/17 - 03/02/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1711.html
Citation Data
DOI : 10.24350/CIRM.V.19116703Cite this video as: Pavlov, Ronnie (2017). Entropy and mixing for multidimensional shifts of finite type - Lecture 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19116703 URI : http://dx.doi.org/10.24350/CIRM.V.19116703 |
See Also
- [Multi angle] Exemple d'Arnoux-Yoccoz, fractal de Rauzy, problème de Novikov : brins d'une guirlande éternelle / Author of the conference Hubert, Pascal.
- [Multi angle] Palindromes patterns / Author of the conference Brlek, Srecko.
- [Post-edited] Entropy and mixing for multidimensional shifts of finite type - Lecture 3 / Author of the conference Pavlov, Ronnie.
- [Post-edited] Entropy and mixing for multidimensional shifts of finite type - Lecture 2 / Author of the conference Pavlov, Ronnie.
Bibliography
- Adams, S., Briceño, R., Marcus, B., & Pavlov, R. (2016). Representation and poly-time approximation for pressure of $\mathbb{Z} ^2$ lattice models in the non-uniqueness region. Journal of Statistical Physics, 162(4), 1031-1067 - http://dx.doi.org/10.1007/s10955-015-1433-4
- Burton, R., & Steif, J.E. (1994). Non-uniqueness of measures of maximal entropy for subshifts of finite type. Ergodic Theory and Dynamical Systems, 14(2), 213-235 - http://dx.doi.org/10.1017/S0143385700007859
- Gamarnik, D., & Katz, D. (2009). Sequential cavity method for computing free energy and surface pressure. Journal of Statistical Physics, 137(2), 205-232 - http://dx.doi.org/10.1007/s10955-009-9849-3
- Marcus, B., & Pavlov, R. (2015). An integral representation for topological pressure in terms of conditional probabilities. Israel Journal of Mathematics, 207(1), 395-433 - http://dx.doi.org/10.1007/s11856-015-1178-4
- Pavlov, R. (2012). Approximating the hard square entropy constant with probabilistic methods. The Annals of Probability, 40(6), 2362-2399 - http://dx.doi.org/10.1214/11-AOP681
