Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On independence and entropy for high-dimensional isotropic subshifts   In this work, we study the problem of finding the asymptotic growth rate of
the number of of $d$-dimensional arrays with side length $n$ over a given
alphabet which avoid a list of one-dimensional "forbidden" words along all
cardinal directions, as both $n$ and $d$ tend to infinity. Louidor, Marcus, and
the second author called this quantity the "limiting entropy"; it is the limit
of a sequence of topological entropies of a sequence of isotropic
$\mathbb{Z}^d$ subshifts with the dimension $d$ tending to infinity. We find an
expression for this limiting entropy which involves only one-dimensional words,
which was implicitly conjectured earlier, and given the name "independence
entropy." In the case where the list of "forbidden" words is finite, this
expression is algorithmically computable and is of the form $\frac{1}{n} \log
k$ for $k,n \in \mathbb{N}$. Our proof also characterizes the weak limits (as
$d \rightarrow \infty$) of isotropic measures of maximal entropy; any such
measure is a Bernoulli extension over some zero entropy factor from an
explicitly defined set of measures. We also demonstrate how our results apply
to various models previously studied in the literature, in some cases
recovering or generalizing known results, but in other cases proving new ones.

28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat