Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Marking (1,2) Points of the Brownian Web and Applications   The Brownian web (BW), which developed from the work of Arratia and then
T\'{o}th and Werner, is a random collection of paths (with specified starting
points) in one plus one dimensional space-time that arises as the scaling limit
of the discrete web (DW) of coalescing simple random walks. Two recently
introduced extensions of the BW, the Brownian net (BN) constructed by Sun and
Swart, and the dynamical Brownian web (DyBW) proposed by Howitt and Warren, are
(or should be) scaling limits of corresponding discrete extensions of the DW --
the discrete net (DN) and the dynamical discrete web (DyDW). These discrete
extensions have a natural geometric structure in which the underlying Bernoulli
left or right "arrow" structure of the DW is extended by means of branching
(i.e., allowing left and right simultaneously) to construct the DN or by means
of switching (i.e., from left to right and vice-versa) to construct the DyDW.
In this paper we show that there is a similar structure in the continuum where
arrow direction is replaced by the left or right parity of the (1,2) space-time
points of the BW (points with one incoming path from the past and two outgoing
paths to the future, only one of which is a continuation of the incoming path).
We then provide a complete construction of the DyBW and an alternate
construction of the BN to that of Sun and Swart by proving that the switching
or branching can be implemented by a Poissonian marking of the (1,2) points.

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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph