Approximating entropy/pressure for multidimensional shifts of finite type

Appears in collection : Multidimensional symbolic dynamics and lattice models of quasicrystals / Dynamique symbolique multidimensionnelle et modèles de quasi-cristaux sur réseau

It has been well-known since foundational work of Hochman and Meyerovitch that that the topological entropy of a multidimensional shift of finite type may have no closed form, and in fact may even be noncomputable. For this reason, it is worthwhile to find provable approximation schemes for the entropy/pressure of "well-behaved" multidimensional models. I will describe some results guaranteeing such approximability schemes, ranging from general results requiring only mixing con-ditions on the underlying SFT to specific results tailored to individual models, and will outline some of the ways in which such results can be proven.

Information about the video

Date of recording 04/04/2024
Date of publication 29/04/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20157903
Cite this video Pavlov, Ronnie (04/04/2024). Approximating entropy/pressure for multidimensional shifts of finite type. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20157903
URL https://dx.doi.org/10.24350/CIRM.V.20157903

Domain(s)

Dynamical Systems

Bibliography

GAMARNIK, David et KATZ, Dmitriy. Sequential cavity method for computing free energy and surface pressure. Journal of Statistical Physics, 2009, vol. 137, p. 205-232. - https://doi.org/10.1007/s10955-009-9849-3
MARCUS, Brian et PAVLOV, Ronnie. Computing bounds for entropy of stationary Z^d Markov random fields. SIAM Journal on Discrete Mathematics, 2013, vol. 27, no 3, p. 1544-1558. - https://doi.org/10.1137/120887382