Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Divide and Color models   In this paper, we initiate the study of "Generalized Divide and Color
Models". A very special interesting case of this is the "Divide and Color
Model" (which motivates the name we use) introduced and studied by Olle
H\"aggstr\"om.
  In this generalized model, one starts with a finite or countable set $V$, a
random partition of $V$ and a parameter $p\in [0,1]$. The corresponding
Generalized Divide and Color Model is the $\{0,1\}$-valued process indexed by
$V$ obtained by independently, for each partition element in the random
partition chosen, with probability $p$, assigning all the elements of the
partition element the value 1, and with probability $1-p$, assigning all the
elements of the partition element the value 0.
  Some of the questions which we study here are the following. Under what
situations can different random partitions give rise to the same color process?
What can one say concerning exchangeable random partitions? What is the set of
product measures that a color process stochastically dominates? For random
partitions which are translation invariant, what ergodic properties do the
resulting color processes have?
  The motivation for studying these processes is twofold; on the one hand, we
believe that this is a very natural and interesting class of processes that
deserves investigation and on the other hand, a number of quite varied
well-studied processes actually fall into this class such as (1) the Ising
model, (2) the fuzzy Potts model, (3) the stationary distributions for the
Voter Model, (4) random walk in random scenery and of course (5) the original
Divide and Color Model.

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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc