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Large deviations for stable like random walks on \(\mathbb Z^d\) with applications to random walks on wreath products. (English) Zbl 1303.60012

The authors derive Donsker-Varadhan-type results for functionals of the occupation times when the underlying random walk on \(\mathbb Z^d\) is in the domain of attraction of an operator-stable law on \(\mathbb R^d\). Applications to random walks on wreath products (also known as lamplighter groups) are given.

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60F10 Large deviations
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