On the Range of a Random Walk

Date

Jun 10, 2014

Time

11:00 AM - 12:00 PM

Speaker

Prof. Davar Khoshnevisan

Affiliation

The University of Utah, Salt Lake City, USA

Series

TUD Mathematik AG Analysis & Stochastik

Language

en

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. R. Schilling

Description

We will present a solution to an open problem of M.T. Barlow and S.J. Taylor (1994) by describing an index which can be used to compute the "large-scale Hausdorff dimension” of the range of an arbitrary random walk on Z^d. A nice byproduct of our methods is a Euclidean form of an old characterization theorem of recurrent sets by J. Lamperti (1963). The basic ideas is to define a “large-scale fractal percolation process,” akin to the Mandelbrot percolation process on $R^d$, and use intersection ideas of Peres (1996) together with potential-theoretic techniques for multi-parameter Markov processes (Khoshnevisan, 2001). The most novel part of our method involves a forest representation of Z^d which might have other uses as well. All terminology, particularly those in quotations, will be defined precisely in the talk. A number of open problems will be presented as well. This is joint work with Nicos Georgiou [Sussex], Kunwoo Kim [Utah], and Alex Ramos [Pernambuco].

Links

• Webseite der AG Analysis & Stochastik

Last modified: Jun 6, 2014, 7:23:23 PM