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Results tagged with pr.probability
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user 37014
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
5
votes
Accepted
Do the order statistics give a good approximation of uniform random variables?
No.
Conditioned on $X_n$, the random variable $n O_n - 1$ is a Binomial random variable with parameters $(n-1, X_n)$. In particular, $O_n$ has fluctuations of order $\sqrt{X_n (1 - X_n)/n}$, so $|X_n …
- 435
4
votes
Accepted
Wasserstein distance between $N(0,1/d)$ and the marginal distribution of $x_1$ when $x=(x_1,...
Let $g \sim N(0, (1/d)I_d)$ be independent of $x$. Then $g_1 \overset{\mathcal L}{=} \|g\| x_1$, so $(x_1, \|g\|x_1)$ is a coupling between the marginal distribution of $x_1$ and $N(0, 1/d)$.
The norm …
- 435
1
vote
Accepted
Does the Gaussian Poincare inequality hold for $p=1$ as well as $p=2$?
Yes, Gaussians also satisfy a Poincaré inequality with $p = 1$ (such an inequality is equivalent to what is called a "Cheeger inequality"). More generally, E. Milman has shown that for log-concave mea …
- 435