Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The critical 2D delta-Bose gas as mixed-order asymptotics of planar
  Brownian motion   We consider the 2D delta-Bose gas by a smooth mollification of the delta
potential, where the coupling constant is in the critical window. The main
result proves that for two particles, the approximate semigroups on $\mathscr
B_b(\Bbb R^2)$ for the Schr\"odinger operator with singular interaction at the
origin converge pointwise in the initial condition. This convergence extends
earlier functional analytic results for the convergence in the $L_2$-norm
resolvent sense. The central methods introduced here apply the excursion theory
of the 2D Bessel process and the ergodicity of the winding number of planar
Brownian motion. The limiting semigroup thus shows both the Kallianpur--Robbins
law for additive functionals of planar Brownian motion and Kasahara's
second-order law for the fluctuations. As an application, the mode of
convergence is extended to the $N$-particle delta-Bose gas for all $N\geq 3$.

37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th