2,143 research outputs found
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
The Influence of Cultural Differences on Chinese College Studentsā Listening Comprehension
In English listening teaching, the background knowledge of teaching material can help the listener improve listening skills. Traditional teaching neglects the teaching of cultural background knowledge, which influences the effect of listening teaching. Understanding the cultural background can help us better understand western culture and improve the effect of listening, thus improving the teaching efficiency. It should also be an important task for students to understand the cultural differences between the east and the west. In view of the current situation of studentsā lack of western culture knowledge, it is an urgent task to strengthen the teaching of Western culture in language teaching
Research of College English Newspaper Reading Teaching Based on the Theory of Implicit Evaluation
Traditional teaching of the English Newspaper reading courses emphasizes the transmission of knowledge and culture, and pays too much attention to the analysis of discourse structures, but ignore the interpretation of the ideology and viewpoints implied in the newspaper discourse. Through the analysis of language resources in China Daily and the Wall Street Journal, we find that there are a lot of implicit evaluation resources in newspapers and periodicals, which indirectly convey the attitudes and opinions of newspaper reporters. Therefore, exploring the implicit evaluation resources in theĀ newspapers in the teaching process is of great significance to cultivate studentsā critical thinking ability and promote the teaching of optional reading courses of English newspapers.
When the geodesic becomes rigid in the directed landscape
When the value of the directed landscape at a point
is sufficiently large, the geodesic from
to is rigid and its location fluctuates of order around
its expectation. We further show that at a midpoint of the geodesic, the
location of the geodesic and the value of the directed landscape after
appropriate scaling converge to two independent Gaussians.Comment: 13 pages, 1 figur
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
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