1,863 research outputs found
Random walks and random fixed-point free involutions
A bijection is given between fixed point free involutions of
with maximum decreasing subsequence size and two classes of vicious
(non-intersecting) random walker configurations confined to the half line
lattice points . In one class of walker configurations the maximum
displacement of the right most walker is . Because the scaled distribution
of the maximum decreasing subsequence size is known to be in the soft edge GOE
(random real symmetric matrices) universality class, the same holds true for
the scaled distribution of the maximum displacement of the right most walker.Comment: 10 page
On ASEP with Step Bernoulli Initial Condition
This paper extends results of earlier work on ASEP to the case of step
Bernoulli initial condition. The main results are a representation in terms of
a Fredholm determinant for the probability distribution of a fixed particle,
and asymptotic results which in particular establish KPZ universality for this
probability in one regime. (And, as a corollary, for the current fluctuations.)Comment: 16 pages. Revised version adds references and expands the
introductio
Dynamics of a tagged particle in the asymmetric exclusion process with the step initial condition
The one-dimensional totally asymmetric simple exclusion process (TASEP) is
considered. We study the time evolution property of a tagged particle in TASEP
with the step-type initial condition. Calculated is the multi-time joint
distribution function of its position. Using the relation of the dynamics of
TASEP to the Schur process, we show that the function is represented as the
Fredholm determinant. We also study the scaling limit. The universality of the
largest eigenvalue in the random matrix theory is realized in the limit. When
the hopping rates of all particles are the same, it is found that the joint
distribution function converges to that of the Airy process after the time at
which the particle begins to move. On the other hand, when there are several
particles with small hopping rate in front of a tagged particle, the limiting
process changes at a certain time from the Airy process to the process of the
largest eigenvalue in the Hermitian multi-matrix model with external sources.Comment: 48 pages, 8 figure
Nonvolatile memory with molecule-engineered tunneling barriers
We report a novel field-sensitive tunneling barrier by embedding C60 in SiO2
for nonvolatile memory applications. C60 is a better choice than ultra-small
nanocrystals due to its monodispersion. Moreover, C60 provides accessible
energy levels to prompt resonant tunneling through SiO2 at high fields.
However, this process is quenched at low fields due to HOMO-LUMO gap and large
charging energy of C60. Furthermore, we demonstrate an improvement of more than
an order of magnitude in retention to program/erase time ratio for a metal
nanocrystal memory. This shows promise of engineering tunnel dielectrics by
integrating molecules in the future hybrid molecular-silicon electronics.Comment: to appear in Applied Physics Letter
An Anisotropic Ballistic Deposition Model with Links to the Ulam Problem and the Tracy-Widom Distribution
We compute exactly the asymptotic distribution of scaled height in a
(1+1)--dimensional anisotropic ballistic deposition model by mapping it to the
Ulam problem of finding the longest nondecreasing subsequence in a random
sequence of integers. Using the known results for the Ulam problem, we show
that the scaled height in our model has the Tracy-Widom distribution appearing
in the theory of random matrices near the edges of the spectrum. Our result
supports the hypothesis that various growth models in dimensions that
belong to the Kardar-Parisi-Zhang universality class perhaps all share the same
universal Tracy-Widom distribution for the suitably scaled height variables.Comment: 5 pages Revtex, 3 .eps figures included, new references adde
Opposite carrier dynamics and optical absorption characteristics under external electric field in nonpolar vs. polar InGaN/GaN based quantum heterostructures
Cataloged from PDF version of article.We report on the electric field dependent carrier dynamics and optical absorption in nonpolar a-plane GaN-based quantum heterostructures grown on r-plane sapphire, which are surprisingly observed to be opposite to those polar ones of the same materials system and similar structure grown on c-plane. Confirmed by their time-resolved photoluminescence measurements and numerical analyses, we show that carrier lifetimes increase with increasing external electric field in nonpolar InGaN/GaN heterostructure epitaxy, whereas exactly the opposite occurs for the polar epitaxy. Moreover, we observe blue-shifting absorption spectra with increasing external electric field as a result of reversed quantum confined Stark effect in these polar structures, while we observe red-shifting absorption spectra with increasing external electric field because of standard quantum confined Stark effect in the nonpolar structures. We explain these opposite behaviors of external electric field dependence with the changing overlap of electron and hole wavefunctions in the context of Fermi's golden rule. (C) 2011 Optical Society of Americ
Edge scaling limits for a family of non-Hermitian random matrix ensembles
A family of random matrix ensembles interpolating between the GUE and the
Ginibre ensemble of matrices with iid centered complex Gaussian
entries is considered. The asymptotic spectral distribution in these models is
uniform in an ellipse in the complex plane, which collapses to an interval of
the real line as the degree of non-Hermiticity diminishes. Scaling limit
theorems are proven for the eigenvalue point process at the rightmost edge of
the spectrum, and it is shown that a non-trivial transition occurs between
Poisson and Airy point process statistics when the ratio of the axes of the
supporting ellipse is of order . In this regime, the family of
limiting probability distributions of the maximum of the real parts of the
eigenvalues interpolates between the Gumbel and Tracy-Widom distributions.Comment: 44 page
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