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Large deviation principles for periodic points of the Dyck shift by Takahasi, Hiroki is a scholarly article available to read on EtoBox.

What is Large deviation principles for periodic points of the Dyck shift about?

We investigate periodic points of the Dyck shift from the viewpoint of large deviations. We establish the level-2 Large Deviation Principle with the rate function given in terms of Kolmogorov-Sinai entropies of shift-invariant Borel probability measures. Unlike topologically mixing Markov shifts, the level-2 rate function is non-convex and level-1 rate functions are superpositions of two convex continuous functions. Using the thermodynamic formalism, we show the analyticity of level-1 rate functions in some relevant cases. We display a non-convex level-1 rate function with a non-differentiable point in the interior of its effective domain.

Author

Takahasi, Hiroki

Published

2025

Language

EN