JuliaMath / JuliaMath/RandomMatrices.jl

TracyWidom beta=4 seems off by a constant

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Julia
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Description

I compared with TracyWidomBeta.jl and also the following random airy operator at beta=4
and those two matched. The code in this package is off by 1.14 or something, if it were the sqrt(2)
(1.41 not 1.14) I might have understood why. Perhaps something in the normalization?
Happy to understand better.

```
function stochastic(β,n)
h=n^-(1/3)
x=h:h:10
N=length(x)
d=(-2/h^2 .- x) + sqrt(4/(h*β))*randn(N) # diagonal
e=fill(1/h^2,N-1) # subdiagonal
eigmax(SymTridiagonal(d,e))
end
```

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Research direction

The issue names no repository file or test; start by locating the package's Tracy-Widom beta=4 implementation and comparing it with TracyWidomBeta.jl and the random airy operator shown. Reproduce the reported offset and inspect the normalization; done means explaining or correcting the discrepancy and confirming matching results.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
data
Issue type
Bug
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
35/100

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