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Results tagged with pr.probability
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user 56325
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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Probability of collision of sums of vectors
Let $S_1$ and $S_2$ be sets of vectors from $\mathbb{R}^d$ that are distinct and let $\sigma(\cdot)$ be a non-linearity, e.g., a componentwise sigmoid function.
Does there exist a random matrix $R \i …
- 321
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vote
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90
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Probability of collision of sums of vectors multiplied by random matrix
Let $S$ and $T$ be sets of vectors from $\mathbb{R}^d$ such that $S$ and $T$ are at least different in one element.
Does there exist a random matrix $M \in \mathbb{R}^{d \times k}$, e.g., a gaussian …
- 321
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answer
708
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Randomly covering a sphere
Let $S$ be the $n$-dimensional unit sphere in the Euclidean space. Further,
let $X_1,\ldots,X_k$ and $Y_1,\ldots,Y_m$ be iid $S$-valued random variables with common (unknown) distribution $\mu$. With …
- 321
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149
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Probability of collision of some family of hash functions
Given $x$ and $y$ in $\mathbb{R}$, and let $\mathcal{H} = \{ h \mid \mathbb{R} \to \mathbb{N} \}$ be a family of hash functions where $ h(x) = \left\lfloor x + \sum^C_{i=1} U_i \right\rfloor$ for some …
- 321