Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One-sided versus two-sided stochastic descriptions   It is well-known that discrete-time finite-state Markov Chains, which are
described by one-sided conditional probabilities which describe a dependence on
the past as only dependent on the present, can also be described as
one-dimensional Markov Fields, that is, nearest-neighbour Gibbs measures for
finite-spin models, which are described by two-sided conditional probabilities.
In such Markov Fields the time interpretation of past and future is being
replaced by the space interpretation of an interior volume, surrounded by an
exterior to the left and to the right.
  If we relax the Markov requirement to weak dependence, that is, continuous
dependence, either on the past (generalising the Markov-Chain description) or
on the external configuration (generalising the Markov-Field description), it
turns out this equivalence breaks down, and neither class contains the other.
In one direction this result has been known for a few years, in the opposite
direction a counterexample was found recently. Our counterexample is based on
the phenomenon of entropic repulsion in long-range Ising (or "Dyson") models.

1
The categories of this paper are: cs
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom