Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariate spatial central limit theorems with applications to
  percolation and spatial graphs   Suppose $X = (X_x, x$ in $Z^d)$ is a family of i.i.d. variables in some
measurable space, $B_0$ is a bounded set in $R^d$, and for $t > 1$, $H_t$ is a
measure on $tB_0$ determined by the restriction of $X$ to lattice sites in or
adjacent to $tB_0$. We prove convergence to a white noise process for the
random measure on $B_0$ given by $t^{-d/2}(H_t(tA)-EH_t(tA))$ for subsets $A$
of $B_0$, as $t$ becomes large,subject to $H$ satisfying a ``stabilization''
condition (whereby the effect of changing $X$ at a single site $x$ is local)
but with no assumptions on the rate of decay of correlations. We also give a
multivariate central limit theorem for the joint distributions of two or more
such measures $H_t$, and adapt the result to measures based on Poisson and
binomial point processes. Applications given include a white noise limit for
the measure which counts clusters of critical percolation, a functional central
limit theorem for the empirical process of the edge lengths of the minimal
spanning tree on random points, and central limit theorems for the on-line
nearest neighbour graph.

25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph