Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Markov Approximations of Gibbs measures for long-range potentials on 1D
  lattices   We study one-dimensional lattice systems with pair-wise interactions of
infinite range. We show projective convergence of Markov measures to the unique
equilibrium state. For this purpose we impose a slightly stronger condition
than summability of variations on the regularity of the interaction. With our
condition we are able to explicitly obtain stretched exponential bounds for the
rate of mixing of the equilibrium state. Finally we show convergence for the
entropy of the Markov measures to that of the equilibrium state via the
convergence of their topological pressure.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th