Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Large Deviations For Randomly Weighted Sums of Random Measures   Let $\{{\bf \mathcal{Z}}_n:n\geq 1\}$ be a sequence of i.i.d. random
probability measures. Independently, for each $n\geq 1$, let $(X_{n1},\ldots,
X_{nn})$ be a random vector of positive random variables that add up to one.
This paper studies the large deviation principles for the randomly weighted sum
$\sum_{i=1}^{n} X_{ni} \mathcal{Z}_i$. In the case of finite Dirichlet weighted
sum of Dirac measures, we obtain an explicit form for the rate function. It
provides a new measurement of divergence between probabilities. As
applications, we obtain the large deviation principles for a class of randomly
weighted means including the Dirichlet mean and the corresponding posterior
mean. We also identify the minima of relative entropy with mean constraint in
both forward and reverse directions.

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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
3
The categories of this paper are: physics