Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Facilitated oriented spin models:some non equilibrium results   We analyze the relaxation to equilibrium for kinetically constrained spin
models (KCSM) when the initial distribution $\nu$ is different from the
reversible one, $\mu$. This setting has been intensively studied in the physics
literature to analyze the slow dynamics which follows a sudden quench from the
liquid to the glass phase. We concentrate on two basic oriented KCSM: the East
model on $\bbZ$, for which the constraint requires that the East neighbor of
the to-be-update vertex is vacant and the model on the binary tree introduced
in \cite{Aldous:2002p1074}, for which the constraint requires the two children
to be vacant. While the former model is ergodic at any $p\neq 1$, the latter
displays an ergodicity breaking transition at $p_c=1/2$. For the East we prove
exponential convergence to equilibrium with rate depending on the spectral gap
if $\nu$ is concentrated on any configuration which does not contain a forever
blocked site or if $\nu$ is a Bernoulli($p'$) product measure for any $p'\neq
1$. For the model on the binary tree we prove similar results in the regime
$p,p'<p_c$ and under the (plausible) assumption that the spectral gap is
positive for $p<p_c$. By constructing a proper test function we also prove that
if $p'>p_c$ and $p\leq p_c$ convergence to equilibrium cannot occur for all
local functions. Finally we present a very simple argument (different from the
one in \cite{Aldous:2002p1074}) based on a combination of combinatorial results
and ``energy barrier'' considerations, which yields the sharp upper bound for
the spectral gap of East when $p\uparrow 1$.

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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
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The categories of this paper are: stat
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph