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Results tagged with pr.probability
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user 197231
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
2
votes
1
answer
187
views
Let $a\in S^d$, $b\in S^{d-1}$ be uniform on the spheres. How to show $\mathbb E[\frac{||a||...
Let $a\in S^d$ and $b\in S^{d-1}$ be points chosen uniformly at random on the $(d+1)$ and $d$-dimensional spheres.
I'm interested in showing some inequalities regarding their norms, the simplest being …
- 55
1
vote
0
answers
72
views
Let $G_{(n)}=(G_1,\ldots,G_n)$ be a vector of $n$ i.i.d. normal vars. How to show $(d+1)(d-1...
Let $G_{(n)}=(G_1,G_2,\ldots,G_{n})$ be a vector of $n$ normal i.i.d. random varibles ($G_i\sim\mathcal N(0,1)$).
How can we show that for all $d\in\mathbb N^+$:
$$
(d+1)\cdot (d-1)\cdot \mathbb E[1/ …
- 55
2
votes
1
answer
127
views
Is $\mathbb E\left[\frac{d}{||x||_1^2}\right]=O(1)$ for all $d\in\mathbb R^+$, where $x\in S...
Let $x\in S^{d-1}$ be chosen uniformly at random from the $d$-dimensional unit sphere.
I want to show that there exists a universal constant $c\in\mathbb R$ such that $\mathbb E\left[\frac{d}{||x||_1^ …
- 55