Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trimming a Tree and the Two-Sided Skorohod Reflection   The $h$-trimming of a tree is a natural regularization procedure which
consists in pruning the small branches of a tree: given $h\geq0$, it is
obtained by only keeping the vertices having at least one leaf above them at a
distance greater or equal to $h$.
  The $h$-cut of a function $f$ is the function of minimal total variation
uniformly approximating the increments of $f$ with accuracy $h$, and can be
explicitly constructed via the two-sided Skorohod reflection of $f$ on the
interval $[0,h]$.
  In this work, we show that the contour path of the $h$-trimming of a rooted
real tree is given by the $h$-cut of its original contour path. We provide two
applications of this result. First, we recover a famous result of Neveu and
Pitman, which states that the $h$-trimming of a tree coded by a Brownian
excursion is distributed as a standard binary tree. In addition, we provide the
joint distribution of this Brownian tree and its trimmed version in terms of
the local time of the two-sided reflection of its contour path. As a second
application, we relate the maximum of a sticky Brownian motion to the local
time of its driving process.

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The categories of this paper are: supr-con
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: econ
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex