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Results tagged with pr.probability
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user 119995
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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Joint distribution of randomly permuted Poisson random variables
Let $U_1, ..., U_n$ be Poisson random variables with rates $ \lambda_1, ..., \lambda_n$ such that $\lambda =\sum_i \lambda_i = O(1)$ (i.e the sum of the rates is bounded). Suppose we have $n$ buckets. …
- 662
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1
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Where does this coupling result use independence when bounding total variational distance?
I am reading this paper, which gives the following coupling result:
Throughout this, I'll assume the dimension $k$ is clear. Let $e_i$ be the $i$-th basis in the $k$ dimensional standard basis.
A $k$ …
- 662
4
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2
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Concentration of $k$-th pairwise distance of random points in a unit square
For $1\leq i \leq n$, let $X_i\sim \text{Uniform}(0,1)$, $Y_i \sim \text{Uniform}(0,1)$ be $n$ points chosen uniformly in the unit square. Denote the $k$-th smallest pairwise distances across the $n$ …
- 662
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Concentration of $k$-th pairwise distance of random points in a unit square
Just came across this paper on arxiv and remembered I posted this question here last year. This is specifically regarding my Question 2. I thought to post an answer.
The authors studied a similar prob …
- 662