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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2602.15455 |
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| _version_ | 1866918342903726080 |
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| author | Chaudhuri, Rohit |
| author_facet | Chaudhuri, Rohit |
| contents | Let $x_1,\dots,x_{n}$ be a fixed sequence of real numbers. At each stage, pick $k$ integers $\{I_{i}\}_{1\leq i \leq k}$ uniformly at random without replacement and then for each $i \in \{1,2,\dots,k\}$ replace $x_{I_i}$ by $(x_{I_1}+x_{I_2}+\dots+x_{I_k})/k$. It is easy to observe that all the co-ordinates converge to $(x_1+\dots+x_n)/n$. In this article, we extend the result of \cite{chatterjee2019note} by establishing order of decay of the expected $L^{2}$ distance. Furthermore, we establish the mixing time to be in between $\frac{n}{k \log k}\log n$ and $\frac{n}{k-1}\log n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15455 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Phase Transition For Repeated K-Averages Chaudhuri, Rohit Probability 60J05 Let $x_1,\dots,x_{n}$ be a fixed sequence of real numbers. At each stage, pick $k$ integers $\{I_{i}\}_{1\leq i \leq k}$ uniformly at random without replacement and then for each $i \in \{1,2,\dots,k\}$ replace $x_{I_i}$ by $(x_{I_1}+x_{I_2}+\dots+x_{I_k})/k$. It is easy to observe that all the co-ordinates converge to $(x_1+\dots+x_n)/n$. In this article, we extend the result of \cite{chatterjee2019note} by establishing order of decay of the expected $L^{2}$ distance. Furthermore, we establish the mixing time to be in between $\frac{n}{k \log k}\log n$ and $\frac{n}{k-1}\log n$. |
| title | A Phase Transition For Repeated K-Averages |
| topic | Probability 60J05 |
| url | https://arxiv.org/abs/2602.15455 |