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High-Frequency Asymptotics for Lipschitz-Killing Curvatures of Excursion Sets on the Sphere
High-Frequency Asymptotics Spherical Ran-dom Fields Gaussian Subordination Lipschitz-Killing Curvatures Minkowski Functionals Excursion Sets
2013/5/2
In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we ...
Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas
Brownian excursion area graph enumeration
2009/5/18
This survey is a collection of various results and formulas by different authors on the areas (integrals) of five related processes, viz. Brownian motion, bridge, excursion, meander and double meander...
The Distribution of Time Spent by a Standard Excursion Above a Given Level, with Applications to Ring Polymers near a Discontinuity in Potential
Standard Brownian Excursions Brownian Bridges Ring Polymers End-Attached Polymers
2009/5/8
The law for the time tau_{a} spent by a standard Brownian excursion above a given level a>0 is found using Ito excursion theory. This is achieved by conditioning the excursion to have exactly one mark...
Invariance Principles for Ranked Excursion Lengths and Heights
excursion lengths excursion heights invariance principle
2009/4/28
In this note we prove strong invariance principles between ranked excursion lengths and heights of a simple random walk and those of a standard Brownian motion. Some consequences concerning limiting d...