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Versions of distributions and naming. What specifically is a "Tracy-Widom distribution". The article starts by specifying "the" Tracy-Widom distribution, but then goes on to mention others also apparently called "Tracy-Widom distributions". So is there more than one distribution function that can be
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Tracy-Widom distributions is skewed in the positive direction, since it's far more likely for the largest eigenvalue to have a spurious fluctuation up rather than down, since then it would have to move against the bulk of the eigenvalues. Can somebody provide an image of a TW distribution?
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defined as the largest eigenvalue of a random
Hermitian matrix; even if that is clear from context, nowhere is the ensemble actually specified. One could use the GUE in the definition, and then ideally mention universality results somewhere as well.
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Can something be said about the asymptotic behaviour of the distribution function at zero and infinity, using simple functions (not something as unusual as the Airy function)?
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pointed out four years ago, there are multiple versions of TW distributions, corresponding to different universality classes of random matrices, such as the
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I messed up on the little-o notation, which should probably just be removed. The source says "oughly, ... the largest eigenvalue is within o(1) of 2σ
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Is this a continuous distribution? The formulation given (without looking elsewhere) leaves open the possibility of a discrete component at zero.
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This makes no sense to me. Saying that something is o(1) means that it goes to zero in the specified limit, i.e. that it is
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called a ""Tracy-Widom distribution"? If there are, can they be specified here in relevant detail?
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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545:. Can someone else clarify whether the o(1) is correct and the text is confused, or vice versa? —
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I will implement this change unless you have any different ideas. Thanks for catching it!
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It also appears as solution of the KPZ equation . Phys. Rev. Lett. 104, 230602 (2010),
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is used to keep the distributions centered at 0. The multiplication by
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bounded below. Something that is bounded both above and below would be
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There is a basic issue in the definition section. Nowhere is
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