Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On multistochastic Monge-Kantorovich problem, bitwise operations, and
  fractals   The multistochastic $ (n,k)$-Monge--Kantorovich problem on a product space
$\prod_{i=1}^n X_i$ is an extension of the classical Monge--Kantorovich
problem. This problem is considered on the space of measures with fixed
projections onto $X_{i_1} \times \ldots \times X_{i_k}$ for all $k$-tuples
$\{i_1, \ldots, i_k\} \subset \{1, \ldots, n\}$ for a given $1 \le k < n$. In
our paper we study well-posedness of the primal and the corresponding dual
problem. Our central result describes a solution $\pi$ to the following
important model case: $n=3, k=2, X_i = [0,1]$, the cost function $c(x,y,z) =
xyz$, and the corresponding two--dimensional projections are Lebesgue measures
on $[0,1]^2$. We prove, in particular, that the mapping $(x,y) \to x \oplus y$,
where $\oplus$ is the bitwise addition (xor- or Nim-addition) on $[0,1] \cong
\mathbb{Z}_2^{\infty}$, is the corresponding optimal transportation. In
particular, the support of $\pi$ is the Sierpi\'nski tetrahedron. In addition,
we describe a solution to the corresponding dual problem.

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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th