All Questions
Tagged with integrable-systems pr.probability
4 questions
2
votes
1
answer
179
views
What is the expectation/variance of the GOE (Airy-1) point process on a partition of the real line?
Let $\chi^{\mathrm{Ai}}(I)$ denote the GUE (Airy-2) point process on the interval $I \subset \mathbb{R}$.
Soshnikov proved
\begin{align}
\mathbb{E}(\chi^{\mathrm{Ai}}(-T, +\infty)) &\sim \...
- 21
3
votes
1
answer
164
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Integrability of complex gaussian random matrix model
It is known that the partition function
$$ \mathcal{Z}_1=\int dH e^{-N{\rm Tr}(H^2)}e^{-NV(H)},$$ where the integral is over $N\times N$ hermitian matrices $H$, with the potential $$ V(H)=\sum_{j\ge 1}...
- 2,552
33
votes
1
answer
1k
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Why does McMahon formula look like the inclusion-exclusion principle?
The McMahon formula for the number of tilings of an $a \times b \times c$ hexagon by lozenges:
$$ \Big[H(a)H(b)H(c)\Big] \Big[H(a+b)H(b+c)H(c+a)\Big]^{-1} \Big[H(a+b+c)\Big]$$
looks oddly like the ...
- 22.8k
2
votes
1
answer
355
views
Why doesn't the argument of circular law convergence of Ginibre spectrum give the same result for GUE?
It appears I am profoundly confused in the following nice argument of Ginibre and Mehta and beautifully presented in Djalil Chafai's blog http://blog.djalil.chafai.net/2010/11/02/aspects-of-the-...
- 4,466