Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Yeah, I understand your point. BTW, I did not mention "dependence structures (like the correlation/copulas)", because for lower bound such terms would naturally appear, so I wonder whether for the upper bound similar phenomenon/structure will also appear. Anyway, I do not think there exists a general result for the upper bound. Thanks.
honestly speaking, no. My aim is to construct an upper bound of Wasserstein distance between two distributions, by using their sub-distributions and dependence structures (like the correlation/copulas). We have formulated similar results of LOWER bounds for lots of distances like Wasserstein and chi2, and now we are interested in the UPPER bounds of Wasserstein. Should you provide any reference about it, I would be rather grateful.
It may be helpful to use generalized tits system. In short for Chevalley groups, G_{x,0} shall be generated by one Iwahori and simple reflections fixing x, while G_x additionally contains elements in fundamental groups fixing x.
@WillSawin Excuse me I am not familiar with etale coverings. So for etale covering f:Y to A^1, the Riemann-Hurwitz implies that \chi(Y)=\chi(A^1)*deg(f) for unramifiedness. Then what should I do after this ? (It seems that the Euler character of Y contains a power of p.) Where could I find these details ?
