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arXiv · 1008.1824

Adiabatic times for Markov chains and applications

Kyle Bradford·Yevgeniy Kovchegov
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Abstract

We state and prove a generalized adiabatic theorem for Markov chains and provide examples and applications related to Glauber dynamics of Ising model over Z^d/nZ^d. The theorems derived in this paper describe a type of adiabatic dynamics for l^1(R_+^n) norm preserving, time inhomogeneous Markov transformations, while quantum adiabatic theorems deal with l^2(C^n) norm preserving ones, i.e. gradually changing unitary dynamics in C^n.

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Kyle Bradford, Yevgeniy Kovchegov. 2010-08-11. Adiabatic times for Markov chains and applications. https://doi.org/10.1007/s10955-011-0219-6

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