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An Excursion from Enumerative Geometry to Solving Systems of Polynomial Equations with Macaulay 2
To solve the polynomial equations mathematics geometry cross theory
2014/12/29
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics ha...
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 ...
Some excursion calculations for reflected Lévy processes
Reflected Levy processes symmetric stable processes exursion theory resolvent density
2009/6/15
Using methods analogous to those introduced in Doney (2005),we express the resolvent density of a(killed)reflected Levy prcess in terms of the resolvent density of the (killed)Levy process. As an appl...
On the scaling limit of simple random walk excursion measure in the plane
Brownian excursion measure Brownian motion simple random walk excursion measure excursion Poisson kernel strong approximation scaling limit
2009/6/12
The Brownian excursion measure is a conformally invariant innite measure on curves. It gured prominently in one of rst major applications of SLE, namely the explicit calculations of the planar Brownia...
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...
Brownian Excursion Conditioned on Its Local Time
Brownian excursion continuum random tree Kingman's coalescent local time
2009/5/8
For a function $ell$ satisfying suitable integrability (but not continuity) requirements, we construct a process $(B^ell_u, 0 leq u leq 1)$ interpretable as Brownian excursion conditioned to have loca...
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...