11,370 research outputs found
Nonequilibrium noise correlations in a point contact of helical edge states
We investigate theoretically the nonequilibrium finite-frequency current
noise in a four-terminal quantum point contact of interacting helical edge
states at a finite bias voltage. Special focus is put on the effects of the
single-particle and two-particle scattering between the two helical edge states
on the fractional charge quasiparticle excitations shown in the nonequilibrium
current noise spectra. Via the Keldysh perturbative approach, we find that the
effects of the single-particle and the two-particle scattering processes on the
current noise depend sensitively on the Luttinger liquid parameter. Moreover,
the Fano factors for the auto- and cross correlations of the currents in the
terminals are distinct from the ones for tunneling between the chiral edge
states in the quantum Hall liquid. The current noise spectra in the
single-particle-scattering-dominated and the two-particle-scattering-dominated
regime are shown. Experimental implications of our results on the transport
through the helical edges in two-dimensional topological insulators are
discussed.Comment: 10 pages, 8 figure
Shape restricted regression with random Bernstein polynomials
Shape restricted regressions, including isotonic regression and concave
regression as special cases, are studied using priors on Bernstein polynomials
and Markov chain Monte Carlo methods. These priors have large supports, select
only smooth functions, can easily incorporate geometric information into the
prior, and can be generated without computational difficulty. Algorithms
generating priors and posteriors are proposed, and simulation studies are
conducted to illustrate the performance of this approach. Comparisons with the
density-regression method of Dette et al. (2006) are included.Comment: Published at http://dx.doi.org/10.1214/074921707000000157 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …