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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 …

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 …

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). …

Note that the Laguerre orthogonal polynomials are in form of [1](bearing combinatoric interpretation) and [3] \begin{align} & L_n^\nu(x)=(-1)^n\sum_{m=0}^n \binom n m \prod_{i=1}^m (\nu+2(n-i))(-x)^{ …

The Hermitian case is more like a state-of-art answer. A good review of results in given in [Holbrook]. $\nu(A,B)\leq\|A-B\|$ for the operator norm. This is a direct consequence from Weyl's inequalit …

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 …

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 …

Non-Gaussianness is an ambiguous concept. In the continuum of probability distributions such as the uniform, where all events are clustered into a given range and equally likely. On the other s …

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, …

There is few posts on MO that asked about reference on this topic, and I found some difficulty during the process of getting myself into the subject so here is the question. I really want to hear fro …

Generally, i want to know what are the main differences between Ergodicity of a stationary Markov chain and non-stationary one? This question could be a better question if formulated better. ( …

"D. P. Bertsekas and S. E. Shreve [39, p. 133] use the term Dynkin system, while P. Billingsley [43] and E. B. Dynkin [111] himself use the term $\lambda$-system. B. Fristedt and L. Gray [129, …

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 trick is to regard the Wiener measure as a random sample function $f(x,t)$ where $x\in (\Omega, \mathscr{F},P)$ and $t\in \mathscr{T}$ is the time index set. Then the whole stochastic process can …

No. Vector space structure is not enough, we actually need a compatible lattice structure to make things work. To apply the conditional expectation operator $E(\bullet\mid Y)$ onto the Hilbert space c …