# Tagged Questions

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### Equivalence of ensembles and $\sum_{N=0}^{\infty} \int_{-Bn}^{\infty} 1_{\text{{N>K or u>A}}}(u)e^{-\beta |\lambda_m|(\frac{u}{2}+n)}du $

I am thinking about a step in the proof of the equivalence of ensembles in StatMech on page 25. step from 3.19 to 3.20.
It seems to be argued there that for $A$ and $K$ large enough, the term
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203 views

### Contour integral (inverse Laplace transform) with arctan

I have what I think is a relatively simple contour integral involving arctan, but it is giving me difficulty. I would really appreciate any help.
The integral itself is, with $\tau$, $\lambda$, and ...

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250 views

### How to perform this matrix integral?

Edit: some backgrouds added.
In quiver matrix model which is reviewed DV or CKR, the path integral reduce to the matrix integral
$$Z \sim \int \prod_{i=1}^r d\Phi_i \prod_{<a,b>} dQ_{ab} ...

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195 views

### Positivity of the Coulomb energy in two dimensions

In dimensions $d\geq 3$ the Coulomb energy is always non-negative (since the Fourier transform of $\frac{1}{|\cdot|^{d-2}}$ is non-negative). What can one say about positivity properties of the ...

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102 views

### Is $C_c(\mathbb{R}^2,\mathbb{R}^2)$ dense in the irrotational square integrable functions?

Let $L_D(\mathbb{R}^n)^n$ be the set of square integrable functions which are the weak derivative of a locally square integrable function. That is
$$L_D(\mathbb{R}^n)^n=\{Du\colon u\in ...