Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized constructive tree weights   The Loop Vertex Expansion (LVE) is a quantum field theory (QFT) method which
explicitly computes the Borel sum of Feynman perturbation series. This LVE
relies in a crucial way on symmetric tree weights which define a measure on the
set of spanning trees of any connected graph. In this paper we generalize this
method by defining new tree weights. They depend on the choice of a partition
of a set of vertices of the graph, and when the partition is non-trivial, they
are no longer symmetric under permutation of vertices. Nevertheless we prove
they have the required positivity property to lead to a convergent LVE; in
fact, we formulate this positivity property precisely for the first time. Our
generalized tree weights are inspired by the Brydges-Battle-Federbush work on
cluster expansions and could be particularly suited to the computation of
connected functions in QFT. Several concrete examples are explicitly given.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga