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Recent publication of Hironaka seems to provoke extended discussions, like Atiyah's proof of almost complex structure of $S^6$ earlier... Unlike Atiyah's paper, Hironaka's paper does not have a histor …

I am now doing an article survey on the field of information geometry started by S.Amari and Barndorff-Nielson. I want to know some research situation in this field. I have read (4) and parts of (3). …

It has been recently mentioned by a speaker (his talk is completely not relevant to random matrix theory/RMT though) that modern statistics, especially random matrices theory, will help solving some n …

If my thinking is wrong please let me know. I have little knowledge on beyond-college physics. For research purposes, I read a few introductions to these three formalisms of classical mechanics [1,2, …

This problem is somehow inspired by a bunch of impressive posts of combinatorial identities by T. Amdeberhan. Earlier this month I learnt from computer scientists that they have a generic algorithmic …

In response to the critical comments below I revised my answer. Hope this is more helpful! (1) Two kinds of metrics are defined on generally different spaces. It is not fair to compare these two met …

The question is clarified by Prof.V.Vovk. See his answer below for discussion. Recently, early works of Gammerman, Vanpnik and Vovk[4] are rediscovered by Wasserman et.al[1] and proposed it as a promi …

While it is known that compact Hausdorff spaces admit unique uniform structures, it is further shown by Johson and Lindenstrauss's result that Banach spaces are characterized by their uniform structur …

First of all I have to express my opinion that the gap between large sample behavior and the finite sample behavior should be considered "unsurprising". Basically speaking, the theory of asymptotics …

First of all, you are mixing many questions into one post... It depends on what do you mean by "generalization". And I am not sure what you mean by talking about "commutative" without mentioning noti …

Due to the supporting hyperplane theorem, a convex set $C$ in a separable topological space has supporting hyperplance at each of its boundary points. The theorem only guarantees its existence, now I …

An ensemble corresponding to a probability distribution usually has finite free energy so it is not a great loss of generality to assume that the ensemble also has finite energy in following discussio …

A very direct result giving characteristic function control for uniform measures on compact convex sets and hence spectrum is [Kulikova& Prokhorov]. It sounds to me that all you want to study is th …

Given a clique complex $K$ constructed from a discrete set of vertices (i.e. its faces are isomorphic to the set of cliques in the 1-skeleton of $K$.), it seems that the Betti numbers $\beta_k$ define …

I do not think Hsu's book is a good place to start with, although it has some strong holds-like details in calculation, neither its depth nor its clarity is comparable to Stroock, Daniel W. An in …