H 1 Entropy and mixing for multidimensional shifts of finite type - Lecture 3

Auteurs : Pavlov, Ronnie (Auteur de la Conférence)
CIRM (Editeur )

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weak special mixing strong special mixing safe symbol computability of measure of maximal entropy sequential cavity method

Résumé : 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.

Codes MSC :
37B10 - Symbolic dynamics
37B40 - Topological entropy
37B50 - Multi-dimensional shifts of finite type, tiling dynamics

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 09/02/2017
    Date de captation : 31/01/17
    Collection : Research schools ; Dynamical Systems and Ordinary Differential Equations
    Format : MP4 (.mp4) - HD
    Durée : 01:04:05
    Domaine : Dynamical Systems & ODE
    Audience : Chercheurs ; Etudiants Science Cycle 2 ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2017-02-02_Pavlov_part3.mp4

Informations sur la rencontre

Nom de la rencontre : New advances in symbolic dynamics / Dynamique symbolique, Combinatoire des mots. Calculabilité. Automates
Organisateurs de la rencontre : Durand, Fabien ; Frid, Anna ; Sablik, Mathieu
Dates : 30/01/2017 - 03/02/17
Année de la rencontre : 2017
URL Congrès : http://conferences.cirm-math.fr/1711.html

Citation Data

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

Voir aussi


  • 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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