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Results tagged with geometric-probability
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user 125275
4
votes
Accepted
Regularity of transport map
This is an open question. The difficulty is that Monge's cost function is very degenerate, so doesn't satisfy the assumptions of the standard regularity theory of optimal transport.
The first difficul …
- 6,001
10
votes
Taking points uniformly inside a general finite geometric domain
For an ellipse, one can rescale the coordinates so that the region becomes a disk and then sample in the way you mentioned.
However, in general sampling efficiently from irregular regions (or distribu …
- 6,001
2
votes
Probabilities of four points being in convex/deltoid configurations
This is not an answer, but was too long to be a comment. The answer will depend on the probability distribution that the points are drawn from. In particular, without even considering the minimum span …
- 6,001
2
votes
Introduction to information geometry and/or geometric control theory
A good place to start learning Information Geometry is the series of blog posts by John Baez, which give an informal survey of some of the central concepts. From there, I think the book by Ay, Jost, L …
- 6,001
3
votes
Approximation of Wasserstein distance between $p_\theta$ and $p_{\theta + d\theta}$
With regard to your first question, one such result shows that under some conditions on $q$, the following inequality holds for all p:
$$W_2(p,q) \leq \sqrt{\frac{ KL(p\parallel q)}\rho}$$
This is a …
