Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metastable behavior for bootstrap percolation on regular trees   We examine bootstrap percolation on a regular (b+1)-ary tree with initial law
given by Bernoulli(p). The sites are updated according to the usual rule: a
vacant site becomes occupied if it has at least theta occupied neighbors,
occupied sites remain occupied forever. It is known that, when b>theta>1, the
limiting density q=q(p) of occupied sites exhibits a jump at some
p_t=p_t(b,theta) in (0,1) from q_t:=q(p_t)<1 to q(p)=1 when p>p_t. We
investigate the metastable behavior associated with this transition.
Explicitly, we pick p=p_t+h with h>0 and show that, as h decreases to 0, the
system lingers around the "critical" state for time order h^{-1/2} and then
passes to fully occupied state in time O(1). The law of the entire
configuration observed when the occupation density is q in (q_t,1) converges,
as h tends to 0, to a well-defined measure.

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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga