Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: log-Coulomb gas with norm-density in $p$-fields   The main result of this paper is a formula for the integral
$$\int_{K^N}\rho(x)\big(\max_{i<j}|x_i-x_j|\big)^a\big(\min_{i<j}|x_i-x_j|\big)^b\prod_{i<j}|x_i-x_j|^{s_{ij}}|dx|,$$
where $K$ is a $p$-field (i.e., a nonarchimedean local field) with canonical
absolute value $|\cdot|$, $N\geq 2$, $a,b\in\mathbb{C}$, the function
$\rho:K^N\to\mathbb{C}$ has mild growth and decay conditions and factors
through the norm $\|x\|=\max_i|x_i|$, and $|dx|$ is the usual Haar measure on
$K^N$. The formula is a finite sum of functions described explicitly by
combinatorial data, and the largest open domain of complex tuples
$(s_{ij})_{i<j}$ on which the integral converges absolutely is given explicitly
in terms of these data and the parameters $a$, $b$, $N$, and $K$. We then
specialize the formula to $s_{ij}=\mathfrak{q}_i\mathfrak{q}_j\beta$, where
$\mathfrak{q}_1,\mathfrak{q}_2,\dots,\mathfrak{q}_N>0$ represent the charges of
an $N$-particle log-Coulomb gas in $K$ with background density $\rho$ and
inverse temperature $\beta$. From this specialization we obtain a mixed-charge
$p$-field analogue of Mehta's integral formula, as well as formulas and
low-temperature limits for the joint moments of $\max_{i<j}|x_i-x_j|$ (the
diameter of the gas) and $\min_{i<j}|x_i-x_j|$ (the minimum distance between
its particles).

32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex