Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical scaling in the matrix model on the Bethe tree   The matrix model with a Bethe-tree embedding space (coinciding at large $N$
with the Kazakov-Migdal ``induced QCD'' model \cite{KM}) is investigated. We
further elaborate the Riemann-Hilbert approach of \rf{Mig1} assuming certain
holomorphic properties of the solution. The critical scaling (an edge
singularity of the density) is found to be $\gamma_{str} = -\frac{1}{\pi}
\arcos D$, for $|D|<1$, and $\gamma_{str} = -\frac{1}{\pi} \arcos
\frac{D}{2D-1}$, for $D>1$. Explicit solutions are constructed at
$D=\frac{1}{2}$ and $D=\infty$.

17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph