Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frozen percolation on the binary tree is nonendogenous   In frozen percolation, i.i.d. uniformly distributed activation times are
assigned to the edges of a graph. At its assigned time, an edge opens provided
neither of its endvertices is part of an infinite open cluster; in the opposite
case, it freezes. Aldous (2000) showed that such a process can be constructed
on the infinite 3-regular tree and asked whether the event that a given edge
freezes is a measurable function of the activation times assigned to all edges.
We give a negative answer to this question, or, using an equivalent formulation
and terminology introduced by Aldous and Bandyopadhyay (2005), we show that the
recursive tree process associated with frozen percolation on the oriented
binary tree is nonendogenous. An essential role in our proofs is played by a
frozen percolation process on a continuous-time binary Galton Watson tree that
has nice scale invariant properties.

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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph