Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence and Concentration of Empirical Measures under Wasserstein
  Distance in Unbounded Functional Spaces   We provide upper bounds of the expected Wasserstein distance between a
probability measure and its empirical version, generalizing recent results for
finite dimensional Euclidean spaces and bounded functional spaces. Such a
generalization can cover Euclidean spaces with large dimensionality, with the
optimal dependence on the dimensionality. Our method also covers the important
case of Gaussian processes in separable Hilbert spaces, with rate-optimal upper
bounds for functional data distributions whose coordinates decay geometrically
or polynomially. Moreover, our bounds of the expected value can be combined
with mean-concentration results to yield improved exponential tail probability
bounds for the Wasserstein error of empirical measures under Bernstein-type or
log Sobolev-type conditions.

29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org