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_posts/2025-03-10-sampling.md
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i.e. **exactly the distribution obtained by first discarding all non‑top‑k items and then sampling categorically inside the top‑k set**.
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### Proof
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Fix any pivot $\tau < \min_{j \in T} p_j$ (true at every step because $\tau$ is always taken from a rejected non‑top‑k item).
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