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- W2592434626 abstract "Consider a stochastic process $(S_{[a_i,b_i]})_{[a_i,b_i] subset mathbb{N}}$, which is indexed by the collection of all nonempty intervals $[a_i,b_i] subset mathbb{N}$ and which is stationary under translations of the intervals. It was shown by M. Hochman that, for any $k geq 1$ and any interval $(alpha,beta) subset mathbb{R}$, one can give an `almost-exponential' bound on the size of the set where the associated process $(S_{[1,n]})_{n geq 1}$ has at least $k$ fluctuations over $(alpha,beta)$. It was also noticed that a similar techniques can be applied in $mathbb{Z}^d$ case. In this article we extend Hochman's upcrossing theorem to groups of polynomial growth." @default.
- W2592434626 created "2017-03-16" @default.
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- W2592434626 date "2016-12-16" @default.
- W2592434626 modified "2023-09-27" @default.
- W2592434626 title "Hochman's upcrossing theorem for groups of polynomial growth" @default.
- W2592434626 hasPublicationYear "2016" @default.
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