705 research outputs found
Stochastic calculus over symmetric Markov processes without time reversal
We refine stochastic calculus for symmetric Markov processes without using
time reverse operators. Under some conditions on the jump functions of locally
square integrable martingale additive functionals, we extend Nakao's
divergence-like continuous additive functional of zero energy and the
stochastic integral with respect to it under the law for quasi-everywhere
starting points, which are refinements of the previous results under the law
for almost everywhere starting points. This refinement of stochastic calculus
enables us to establish a generalized Fukushima decomposition for a certain
class of functions locally in the domain of Dirichlet form and a generalized
It\^{o} formula. (With Errata.)Comment: Published in at http://dx.doi.org/10.1214/09-AOP516 and Errata at
http://dx.doi.org/10.1214/11-AOP700 the Annals of Probability
(http://www.imstat.org/aop/) by the Institute of Mathematical Statistics
(http://www.imstat.org
A topological splitting theorem for weighted Alexandrov spaces
Under an infinitesimal version of the Bishop-Gromov relative volume
comparison condition for a measure on an Alexandrov space, we prove a
topological splitting theorem of Cheeger-Gromoll type. As a corollary, we prove
an isometric splitting theorem for Riemannian manifolds with singularities of
nonnegative (Bakry-Emery) Ricci curvature.Comment: 20 pages to appear in Tohoku Mathematical Journa
Two-dimensional Non-Hermitian Delocalization Transition as a Probe for the Localization Length
When one applies a type of non-Hermitian effect, constant imaginary vector
potential, to disordered systems, delocalization is induced even in two or
lower dimension. By using the non-Hermitian induced transition as a probe, We
propose a new procedure of estimating localization in arbitrary-dimensional
systems. By examining numerically the two-dimensional non-Hermitian
tight-biding model with onsite disorder, it is shown that the failure of
absorbing the non-Hermitian effect, namely the breakdown of the imaginary gauge
transformation, characterize the inverse localization length near the band
center.Comment: 4 pages, 4 fig
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