208,957 research outputs found
Brownian motion in attenuated or renormalized inverse-square Poisson potential
We consider the parabolic Anderson problem with random potentials having
inverse-square singularities around the points of a standard Poisson point
process in , . The potentials we consider are obtained
via superposition of translations over the points of the Poisson point process
of a kernel behaving as near the origin, where . In order to make
sense of the corresponding path integrals, we require the potential to be
either attenuated (meaning that is integrable at infinity) or,
when , renormalized, as introduced by Chen and Kulik in [8]. Our main
results include existence and large-time asymptotics of non-negative solutions
via Feynman-Kac representation. In particular, we settle for the renormalized
potential in the problem with critical parameter , left
open by Chen and Rosinski in [arXiv:1103.5717].Comment: 36 page
Gluon polarization in the nucleon demystified
Recently, X. Chen et al. proposed a new approach to the gauge invariant
decomposition of the nucleon spin into helicity and orbital parts. The key
ingredient in their construction is the separation of the gauge field into
`physical' and `pure gauge' parts. We suggest a simple separation scheme and
show that the resulting gluon helicity coincides with the first moment of the
conventional polarized gluon distribution measurable in high energy
experiments.Comment: 6 page
Large deviations for self-intersection local times of stable random walks
Let be a random walk on . Let the local time at the state and the q-fold self-intersection local
time (SILT). In \cite{Castell} Castell proves a large deviations principle for
the SILT of the simple random walk in the critical case . In the
supercritical case , Chen and M\"orters obtain in \cite{ChenMorters}
a large deviations principle for the intersection of independent random
walks, and Asselah obtains in \cite{Asselah5} a large deviations principle for
the SILT with . We extend these results to an -stable process
(i.e. ) in the case where .Comment: 22 page
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