Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gibbs measures on mutually interacting Brownian paths under
  singularities   We are interested in the analysis of Gibbs measures defined on two
independent Brownian paths in $\mathbb R^d$ interacting through a mutual
self-attraction. This is expressed by the Hamiltonian $\int\int_{\mathbb
R^{2d}} V(x-y) \mu(d x)\nu(d y)$ with two probability measures $\mu$ and $\nu$
representing the occupation measures of two independent Brownian motions. We
will be interested in class of potentials $V$ which are {\it{singular}}, e.g.,
Dirac or Coulomb type interactions in $\mathbb R^3$, or the correlation
function of the parabolic Anderson problem with white noise potential.
  The mutual interaction of the Brownian paths inspires a compactification of
the quotient space of orbits of product measures, which is structurally
different from the self-interacting case introduced in \cite{MV14}, owing to
the lack of shift-invariant structure in the mutual interaction. We prove a
{\it{strong large deviation principle}} for the product measures of two
Brownian occupation measures in such a compactification, and derive asymptotic
path behavior under Gibbs measures on Wiener paths arising from mutually
attracting singular interactions. For the spatially smoothened parabolic
Anderson model with white noise potential, our analysis allows a direct
computation of the annealed Lyapunov exponents and a strict ordering of them
implies the {\it{intermittency effect}} present in the smoothened model.

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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int