Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Phase Transition and Stochastic Domination in Pippenger's
  Probabilistic Failure Model for Boolean Networks with Unreliable Gates   We study Pippenger's model of Boolean networks with unreliable gates. In this
model, the conditional probability that a particular gate fails, given the
failure status of any subset of gates preceding it in the network, is bounded
from above by some $\epsilon$. We show that if we pick a Boolean network with
$n$ gates at random according to the Barak-Erd\H{o}s model of a random acyclic
digraph, such that the expected edge density is $c n^{-1}\log n$, and if
$\epsilon$ is equal to a certain function of the size of the largest reflexive,
transitive closure of a vertex (with respect to a particular realization of the
random digraph), then Pippenger's model exhibits a phase transition at $c=1$.
Namely, with probability $1-o(1)$ as $n\to\infty$, we have the following: for
$0 \le c \le 1$, the minimum of the probability that no gate has failed, taken
over all probability distributions of gate failures consistent with Pippenger's
model, is equal to $o(1)$, whereas for $c >1$ it is equal to
$\exp(-\frac{c}{e(c-1)}) + o(1)$. We also indicate how a more refined analysis
of Pippenger's model, e.g., for the purpose of estimating probabilities of
monotone events, can be carried out using the machinery of stochastic
domination.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom