On the average of the Airy process and its time reversal

We show that the supremum of the average of the Airy process and its time reversal minus a parabola is distributed as the maximum of two independent GUE Tracy-Widom random variables. The proof is obtained by considering a directed last passage percolation model with a rotational symmetry in two different ways. We also review other known identities between the Airy process and the Tracy-Widom distributions.Comment: 12 page

Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes

We show that the ratio of a discrete Toeplitz/Hankel determinant and its continuous counterpart equals a Freholm determinant involving continuous orthogonal polynomials. This identity is used to evaluate a triple asymptotic of some discrete Toeplitz/Hankel determinants which arise in studying non-intersecting processes. We show that the asymptotic fluctuations of the width of such processes are given by the GUE Tracy-Widom distribution. This result leads us to an identity between the GUE Tracy-Widom distribution and the maximum of the sum of two independent Airy processes minus a parabola. We provide an independent proof of this identity.Comment: 30 pages, 3 figure

Fluctuations of TASEP and LPP with general initial data

We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage percolation from a general lattice path to a point. We also consider variants of last passage percolation with inhomogeneous parameter geometric weights and provide variational formulas of a similar nature. This proves one aspect of the conjectural description of the renormalization fixed point of the Kardar-Parisi-Zhang universality class.Comment: 44 pages, 6 figure

Global-Scale Resource Survey and Performance Monitoring of Public OGC Web Map Services

One of the most widely-implemented service standards provided by the Open Geospatial Consortium (OGC) to the user community is the Web Map Service (WMS). WMS is widely employed globally, but there is limited knowledge of the global distribution, adoption status or the service quality of these online WMS resources. To fill this void, we investigated global WMSs resources and performed distributed performance monitoring of these services. This paper explicates a distributed monitoring framework that was used to monitor 46,296 WMSs continuously for over one year and a crawling method to discover these WMSs. We analyzed server locations, provider types, themes, the spatiotemporal coverage of map layers and the service versions for 41,703 valid WMSs. Furthermore, we appraised the stability and performance of basic operations for 1210 selected WMSs (i.e., GetCapabilities and GetMap). We discuss the major reasons for request errors and performance issues, as well as the relationship between service response times and the spatiotemporal distribution of client monitoring sites. This paper will help service providers, end users and developers of standards to grasp the status of global WMS resources, as well as to understand the adoption status of OGC standards. The conclusions drawn in this paper can benefit geospatial resource discovery, service performance evaluation and guide service performance improvements.Comment: 24 pages; 15 figure

Dust-acoustic waves and stability in the permeating dusty plasma: II. Power-law distributions

The dust-acoustic waves and their stability driven by a flowing dusty plasma when it cross through a static (target) dusty plasma (the so-called permeating dusty plasma) are investigated when the components of the dusty plasma obey the power-law q-distributions in nonextensive statistics. The frequency, the growth rate and the stability condition of the dust-acoustic waves are derived under this physical situation, which express the effects of the nonextensivity as well as the flowing dusty plasma velocity on the dust-acoustic waves in this dusty plasma. The numerical results illustrate some new characteristics of the dust-acoustic waves, which are different from those in the permeating dusty plasma when the plasma components are the Maxwellian distribution. In addition, we show that the flowing dusty plasma velocity has a significant effect on the dust-acoustic waves in the permeating dusty plasma with the power-law q-distribution.Comment: 20 pages, 10 figures, 41 reference