Please use this identifier to cite or link to this item:
https://hdl.handle.net/20.500.12202/9590
Title: | Limit theorems for low dimensional generalized $(T,T^{-1})$ transformations |
Authors: | Dolgopyat, Dmitry Dong, Changguang Kanigowski, Adam Nandori, Peter 0000-0001-8238-6653 |
Keywords: | Mathematics - Dynamical Systems |
Issue Date: | 2023 |
Citation: | Limit theorems for low dimensional generalized transformations D Dolgopyat, C Dong, A Kanigowski, P Nandori arXiv preprint arXiv:2305.04246 |
Abstract: | We consider generalized $(T, T^{-1})$ transformations such that the base map satisfies a multiple mixing local limit theorem and anticoncentration large deviation bounds and in the fiber we have $\mathbb{R}^d$ actions with $d=1$ or $2$ which are exponentially mixing of all orders. If the skewing cocycle has zero drift, we show that the ergodic sums satisfy the same limit theorems as the random walks in random scenery studied by Kesten and Spitzer (1979) and Bolthausen (1989). The proofs rely on the quenched CLT for the fiber action and the control of the quenched variance. This paper complements our previous work where the classical central limit theorem is obtained for a large class of generalized $(T, T^{-1})$ transformations. |
Description: | Scholarly article / OA (arXiv PDF) |
URI: | http://arxiv.org/abs/2305.04246 https://hdl.handle.net/20.500.12202/9590 |
Appears in Collections: | Stern College for Women -- Faculty Publications |
Files in This Item:
File | Description | Size | Format | |
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Nandori OA arXiv 2023 Limit theorems 2305.04246.pdf | 326.88 kB | Adobe PDF | View/Open |
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