Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical inference for Bures-Wasserstein barycenters   In this work we introduce the concept of Bures-Wasserstein barycenter $Q_*$,
that is essentially a Fr\'echet mean of some distribution $\mathbb{P}$
supported on a subspace of positive semi-definite Hermitian operators
$\mathbb{H}_{+}(d)$. We allow a barycenter to be restricted to some affine
subspace of $\mathbb{H}_{+}(d)$ and provide conditions ensuring its existence
and uniqueness. We also investigate convergence and concentration properties of
an empirical counterpart of $Q_*$ in both Frobenius norm and Bures-Wasserstein
distance, and explain, how obtained results are connected to optimal
transportation theory and can be applied to statistical inference in quantum
mechanics.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin