Random walks and random fixed-point free involutions

A bijection is given between fixed point free involutions of $\{1,2,...,2N\}$ with maximum decreasing subsequence size $2p$ and two classes of vicious (non-intersecting) random walker configurations confined to the half line lattice points $l \ge 1$. In one class of walker configurations the maximum displacement of the right most walker is $p$. 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 $(1+1)$ 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 $n\times n$ 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 $n^{-1/3}$. 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