Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contraction of the proximal map and generalized convexity of the
  Moreau-Yosida regularization in the 2-Wasserstein metric   We investigate the Moreau-Yosida regularization and the associated proximal
map in the context of discrete gradient flow for the 2-Wasserstein metric. Our
main results are a stepwise contraction property for the proximal map and an
"above the tangent line" inequality for the regularization. Using the latter,
we prove a Talagrand inequality and an HWI inequality for the regularization,
under appropriate hypotheses. In the final section, the results are applied to
study the discrete gradient flow for R\'enyi entropies. As Otto showed, the
gradient flow for these entropies in the 2-Wasserstein metric is a porous
medium flow or a fast diffusion flow, depending on the exponent of the entropy.
We show that a striking number of the remarkable features of the porous medium
and fast diffusion flows are present in the discrete gradient flow and do not
simply emerge in the limit as the time-step goes to zero.

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The categories of this paper are: nlin
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
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The categories of this paper are: cs