Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fluctuations of the Gromov-Prohorov sample model   In this paper, we study the fluctuations of observables of metric measure
spaces which are random discrete approximations $X_n$ of a fixed arbitrary
(complete, separable) metric measure space $X=(\mathcal{X},d,\mu)$. These
observables $\Phi(X_n)$ are polynomials in the sense of
Greven-Pfaffelhuber-Winter, and we show that for a generic model space $X$,
they yield asymptotically normal random variables. However, if $X$ is a compact
homogeneous space, then the fluctuations of the observables are much smaller,
and after an adequate rescaling, they converge towards probability
distributions which are not Gaussian. Conversely, we prove that if all the
fluctuations of the observables $\Phi(X_n)$ are smaller than in the generic
case, then the measure metric space $X$ is compact homogeneous. The proofs of
these results rely on the Gromov reconstruction principle, and on an adaptation
of the method of cumulants and mod-Gaussian convergence developed by
F\'eray-M\'eliot-Nikeghbali.

15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
9
The categories of this paper are: nlin