6,158 research outputs found
One-sided L\'{e}vy stable distributions
In this paper, we show new representations of one-sided L\'{e}vy stable
distributions for irrational L\'{e}vy indices of the type
which are not covered in
\cite{pg1} : for rational L\'{e}vy indices. Furthermore, other equivalent
representations for a distribution of a rational L\'{e}vy index is described.
We also give a simplest proof for the formulae which cover the cases for
rational L\'{e}vy indices. Finally we introduce the concepts of L\'{e}vy
smashing and L\'{e}vy-smashed gamma stochastic processes.Comment: Welcome for comment
c-theorem of the entanglement entropy
We holographically investigate the renormalization group flow in a
two-dimensional conformal field theory deformed by a relevant operator. If the
relevant operator allows another fixed point, the UV conformal field theory
smoothly flows to a new IR conformal field theory. From the holographic point
of view, such a renormalization group flow can be realized as a dual geometry
interpolating two different AdS boundaries. On this interpolating geometry, we
investigate how the c-function of the entanglement entropy behaves along the RG
flow analyt- ically and numerically, which reproduces the expected central
charges of UV and IR. We also show that the c-function monotonically decreases
from UV to IR without any phase transition.Comment: 24 pages, 8 figure
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