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Proving the Replica Trick works

The replica trick attempts to calculate the expectation of the logarithm $X=\log(Z)$ of a random variable $Z$. The wikipedia article describes the logarithm as the limit $$ \log(Z) = \lim_{n\to 0}\...
Felix Benning's user avatar
6 votes
0 answers
398 views

semiclassical proof of Wigner semicircle

In Terence Tao's discussion of the Gaussian Unitary Ensemble, he derives the Dyson and Airy kernels. The GUE is the probability distribution of the eigenvalues of a random Hermitian matrix. \[ \int ...
john mangual's user avatar
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4 votes
3 answers
644 views

Traceless GUE : Four Centered Fermions

The proof of the Wigner Semicircle Law comes from studying the GUE Kernel $$ K_N(\mu, \nu)=e^{-\frac{1}{2}(\mu^2+\nu^2)} \cdot \frac{1}{\sqrt{\pi}} \sum_{j=0}^{N-1}\frac{H_j(\lambda)H_j(\mu)}{2^j j!} ...
john mangual's user avatar
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0 votes
0 answers
59 views

Convergence of Liouville correlation functions

A key object in Liouville conformal field theory is the random Liouville measure $M$ defined heuristically as $M(d^2x) = :e^{2bX(x)}: d^2x$, where $X$ is a Gaussian free field and $:e^{2bX}:$ denotes ...
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