Entropy and mixing for multidimensional shifts of finite type - Lecture 3 | Vidéo | Carmin.tv

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Entropy and mixing for multidimensional shifts of finite type - Lecture 3

By Ronnie Pavlov

Appears in collections : New advances in symbolic dynamics / Dynamique symbolique, Combinatoire des mots. Calculabilité. Automates, Ecoles de recherche

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.

Information about the video

Date of recording 31/01/2017
Date of publication 09/02/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19117403
Cite this video Pavlov, Ronnie (31/01/2017). Entropy and mixing for multidimensional shifts of finite type - Lecture 3. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19117403
URL https://dx.doi.org/10.24350/CIRM.V.19117403

Domain(s)

Dynamical Systems

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

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