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How should this article treat the Wishart distribution?
- The probability distribution of random matrices that is most widely known (i.e. the Wishart distribution);
- the probability distributions studied by those who in the present day identify their field of research as "random matrices"
are two different things. The latter group have hijacked the term "random matrices". Of course, it is only out of ignorance that they have done so. This article should remedy their ignorance by giving some prominence to the various probability distributions of random matrices that are conventionally studied, including the Wishart distribution and others. Michael Hardy (talk) 17:14, 1 March 2009 (UTC)
- ...a qualification to my remarks above: I see Persi Diaconis cited in the article. I certainly don't mean to imply that he is ignorant of the Wishart distribution. He's not. And I'm pretty sure Andrew Odlyzko knows the Wishart distribution exists, although I suppose he probably knows far less about it that Percy Diaconis does. But lots of people getting seduced into this field of research don't know such things. Michael Hardy (talk) 17:18, 1 March 2009 (UTC)
- The article contained many interesting things, but without any apparent order. I have tried to make it much shorter and accessible. On the way I deleted quite a few things, and rearranged other parts, mainly since I thought they were -- as written -- only accessible to experts. Now the problem is opposite: many important parts are missing completely. So critical comments and ideas are most welcome. Sasha (talk) 01:37, 1 May 2011 (UTC)
- The normalisation of GUE is different in several places, e.g., it differs here from the one in Determinantal point process. I do not know which one is better, but I guess some uniformisation is needed. Sasha (talk) 04:47, 3 May 2011 (UTC)
- The section "other applications" mainly repeated things which appeared in other parts. One section with ref-s (rather than 3) should be enough, I believe. I also erased a few things which looked to me as part of ongoing research. If you feel that I erased something crucial, please comment. Sasha (talk) 23:36, 14 May 2011 (UTC)
The section "major applications" needs a major clean-up. I have tried to erase it completely, but encountered resistance, so perhaps this is the place to discuss it in more detail.
For now, I have erased the lines that are obviously redundant (appear in almost the same wording in other parts of the article). What is left needs to be classified (physics moved to physics, et cet.); also, many lines lack citations. Fellow editors, please help revise this part.
- CLT for linear statistics
- local regime: edge (+ link to Tracy--Widom)
Having worked myself on various mentioned random matrix finance models, I'd say the methodology is not uncommon. It is advanced but well used. Even APTs model is no big deal!
It would be useful to know the important commercial models.
Portions could be made more accessible
For example, I found this comment in a StackExchange discussion:
In Random Matrix Theory, for example, Gaussian ensembles are frequently studied, where matrix entries are independent normally distributed (complex) numbers, subject to some symmetry constraints (Hermiticity for example) — and this is a well-specified problem.
Is that right? There's nothing so clear to the non-specialist in this article as it stands.
The lead doesn't even address the first concern of a mathematically astute non-specialist: how is "random" even defined in the matrix setting?
Is it just element-wise over some specified distribution, or are distributions defined over the entire set of matrices not reductive to this?
I'm guessing that "subject to some symmetry constraints" is such a thing. As a computer scientist, I've often seen naive element-wise generation with true/false post-filtering (e.g. fill a matrix with independent normal complex, then throw away the non-Hermits). But even that won't work (unsafe at any speed) if the distribution is really defined at the matrix level.
Wikipedia is where I go when I don't want to puzzle out GUE(n) like a bad dream where I'm back at grad school. — MaxEnt 19:41, 28 December 2016 (UTC)