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arXiv · 2401.05118

On Escape rate for subshift with Markov measure

Nikita Agarwal·Haritha Cheriyath·Sharvari Neetin Tikekar
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Abstract

In this paper, we consider a subshift of finite type with Markov measure. By considering a union of cylinders as holes, we investigate the exponential growth rate of measure of points whose orbits do not escape into the hole over a fixed number of iterations. We present two formulations for this escape rate: one based on the spectral radius of the Hadamard product of a related adjacency matrix and the stochastic matrix with respect to which the Markov measure is defined, and the other utilizing a recurrence relation. These formulations enable a comparative analysis of escape rates into distinct holes.

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Nikita Agarwal, Haritha Cheriyath, Sharvari Neetin Tikekar. 2024-01-10. On Escape rate for subshift with Markov measure. https://arxiv.org/abs/2401.05118

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