Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit heat kernels of a model of distorted Brownian motion on spaces
  with varying dimension   In this paper, we study a particular model of distorted Brownian motion (dBM)
on state spaces with varying dimension. Roughly speaking, the state space of
such a process consists of two components: a $3$-dimensional component and a
$1$-dimensional component. These two parts are joined together at the origin.
The restriction of dBM on the $3$- or $1$-dimensional component receives a
strong "push" towards the origin. On each component, the "magnitude" of the
"push" can be parametrized by a constant $\gamma >0$. In this article, using
probabilistic method, we get the exact expressions for the transition density
functions of dBM with varying dimension for any $0<t<\infty$.

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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph