Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-field lattice trees   We introduce a mean-field model of lattice trees based on embeddings into
$\Z^d$ of abstract trees having a critical Poisson offspring distribution. This
model provides a combinatorial interpretation for the self-consistent
mean-field model introduced previously by Derbez and Slade, and provides an
alternate approach to work of Aldous. The scaling limit of the mean-field model
is integrated super-Brownian excursion (ISE), in all dimensions. We also
introduce a model of weakly self-avoiding lattice trees, in which an embedded
tree receives a penalty $e^{-\beta}$ for each self-intersection. The weakly
self-avoiding lattice trees provide a natural interpolation between the
mean-field model ($\beta=0$), and the usual model of strictly self-avoiding
lattice trees ($\beta=\infty$) which associates the uniform measure to the set
of lattice trees of the same size.

19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci