The Third and Fourth Moment of the Renormalized Intersection Local Time

2014/11/29 by Daniel Höf, Höf, Daniel
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.PR #msc:60J10 #msc:60J65

paper · pdf · doi:10.48550/arxiv.1412.0090

11 pages

arxiv created 2014/11/29 · arxiv updated 2014/12/02

Abstract

In this article we calculate the third and fourth moment of the renormalized intersection local time of a planar Brownian motion. The third moment is calculated anlaytically, the fourth moment numerically. For the closed planar random walk the third moment of the distribution of the multiple point range is also calculated in leading order.

Related

• The Characteristic Function of the Renormalized Intersection Local Time of the Planar Brownian Motion
• An almost sure invariance principle for renormalized intersection local times
• An almost sure invariance principle for the range of planar random walks
• Renormalization and convergence in law for the derivative of intersection local time in R²
• A limit theorem for moments in space of the increments of Brownian local time