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arXiv · 2310.17105

Non-stationary It\^o-Kawada and Ergodic Theorems for random isometries

Grigorii Monakov
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Abstract

We consider a nonstationary sequence of independent random isometries of a compact metrizable space. Assuming that there are no proper closed subsets with deterministic image we establish a weak-* convergence to the unique invariant under isometries measure, Ergodic Theorem and Large Deviation Type Estimate. We also show that all the results can be carried over to the case of a random walk on a compact metrizable group. In particular, we prove a nonstationary analog of classical It\^o-Kawada theorem and give a new alternative proof for the stationary case.

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Grigorii Monakov. 2023-10-26. Non-stationary It\^o-Kawada and Ergodic Theorems for random isometries. https://arxiv.org/abs/2310.17105

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