Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local structure of multi-dimensional martingale optimal transport   This paper analyzes the support of the conditional distribution of optimal
martingale transport plans in higher dimension. In the context of a distance
coupling in dimension larger than 2, previous results established by Ghoussoub,
Kim & Lim show that this conditional transport is concentrated on its own
Choquet boundary. Moreover, when the target measure is atomic, they prove that
the support is concentrated on d+1 points, and conjecture that this result is
valid for arbitrary target measure.
  We provide a structure result of the support of the conditional optimal
transport for general Lipschitz couplings. Using tools from algebraic geometry,
we provide sufficient conditions for finiteness of this conditional support,
together with (optimal) lower bounds on the maximal cardinality for a given
coupling function. More results are obtained for specific examples of coupling
functions based on distance functions. In particular, we show that the above
conjecture of Ghoussoub, Kim & Lim is not valid beyond the context of atomic
target distributions.

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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: physics