N叉树上的离散时间量子随机行走

通过离散时间量子随机行走的框架,我们研究了在N叉树上的离散时间量子随机行走,该框架不需要硬币空间,仅仅只需要选择一个除了酉性再无其它限制的演化算子,并且包含了使用再生结构的轨道枚举和z变换.作为结果,我们在封闭形式中计算了在根处的振幅的生成函数.     

带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*

本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L²(?, L²_σ(R)).     

Covering with blocks in the non-symmetric case

Considering an infinite string of i.i.d. random letters drawn from a finite alphabet we define the cover timeW _n as the number of random letters needed until each pattern of lenghtn appears at least once as a substring. Sharp weak and a.s. limit results onW _n are known in the symmetric case, i.e., when the random letters are uniformly distributed over the alphabet. In this paper we determine the limit distribution ofW _n in the nonsymmetric case asn. Generalizations in terms of point processes are also proved.Dedicated to Endre Csáki on his 60th birthday.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.     

Self-avoiding walks and trees in spread-out lattices

LetG _R be the graph obtained by joining all sites ofZ ^d which are separated by a distance of at mostR. Let (G _R ) denote the connective constant for counting the self-avoiding walks in this graph. Let (G _R ) denote the coprresponding constant for counting the trees embedded inG _R . Then asR, (G _R ) is asymptotic to the coordination numberk _R ofG _R , while (G _R ) is asymptotic toek _R. However, ifd is 1 or 2, then (G _R )-k _R diverges to –.Dedicated to Oliver Penrose on this occasion of his 65th birthday.     

On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.     

一种基于熵源分离模型的可重构安全原语

在信息爆炸时代,信息的安全问题受到了广泛关注。在物联网设备的加密协议中,物理不可克隆函数(PUF)与真随机数发生器成为加密协议中基本的安全原语,提供了轻量级的解决方案。文章提出了一种熵源分离模型,能够分离环形振荡器中抖动(真随机数发生器的熵)和工艺偏差(PUF熵)引起的延时。基于该模型,在FPGA上设计了一种可重构的双工作模式电路,通过改变模式可分别生成PUF和真随机数。相较于FPGA上独立设计的PUF和真随机数发生器,该结构具有资源开销小、面积利用率高、功耗低等优势。实验结果表明,生成的PUF稳定性高、唯一性强、均匀性好;真随机数序列均通过了NIST测试,具有高随机性和不可预测性。     

One-Component Artificial Gustatory System Based on Hydrogen-Bond Organic Framework for Discrimination of Versatile Analytes

Hydrogen-bond organic frameworks (HOFs) with excellent structural and luminescent properties have emerged as a promising material for the construction of fluorescence sensors. However, designing a facile, universal and high throughput sensor with multiplex detection capacity still remains challenging. Herein, a one-component sensor array is constructed that mimics natural gustatory system for accurate and high-throughput discrimination and identification of versatile analytes. HOF as a single sensing element greatly simplifies the probe preparation in sensor array and detection procedure. Metal ions, proteins and bacteria as the model targets are rapid and accurately discriminated, presenting the universality of the system. Particularly, the system is successfully used for the classification of antibiotic mechanisms. The study expands the application scope of HOFs and provides a facile and universal system for sensing applications.     

Laser-Printed Plasmonic Metasurface Supporting Bound States in the Continuum Enhances and Shapes Infrared Spontaneous Emission of Coupled HgTe Quantum Dots

In order to advance the development of quantum emitter-based devices, it is essential to enhance light-matter interactions through coupling between semiconductor quantum dots with high quality factor resonators. Here, efficient tuning of the emission properties of HgTe quantum dots in the infrared spectral region is demonstrated by coupling them to a plasmonic metasurface that supports bound states in the continuum. The plasmonic metasurface, composed of an array of gold nanobumps, is fabricated using single-step direct laser printing, opening up new opportunities for creating exclusive 3D plasmonic nanostructures and advanced photonic devices in the infrared region. A 12-fold enhancement of the photoluminescence in the 900–1700 nm range is observed under optimal coupling conditions. By tuning the geometry of the plasmonic arrays, controllable shaping of the emission spectra is achieved, selectively enhancing specific wavelength ranges across the emission spectrum. The observed enhancement and shaping of the emission are attributed to the Purcell effect, as corroborated by systematic measurements of radiative lifetimes and optical simulations based on the numerical solution of Maxwell's equations. Moreover, coupling of the HgTe photoluminescence to high quality factor modes of the metasurface improves emission directivity, concentrating output within an ≈20° angle.