Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Synchronous couplings of reflected Brownian motions in smooth domains   For every bounded planar domain $D$ with a smooth boundary, we define a
`Lyapunov exponent' $\Lambda(D)$ using a fairly explicit formula. We consider
two reflected Brownian motions in $D$, driven by the same Brownian motion
(i.e., a `synchronous coupling'). If $\Lambda(D)>0$ then the distance between
the two Brownian particles goes to 0 exponentially fast with rate $\Lambda
(D)/(2|D|)$ as time goes to infinity. The exponent $\Lambda(D)$ is strictly
positive if the domain has at most one hole. It is an open problem whether
there exists a domain with $\Lambda(D)<0$.

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The categories of this paper are: stat
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The categories of this paper are: econ
25
The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an