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UNIVERSITY OF REGINA Department of Mathematics and Statistics
 

Summary: UNIVERSITY OF REGINA
Department of Mathematics and Statistics
Graduate Student Seminar
SPEAKER: Luis Diego Leon Chi
DATE: 05 December 2006
TIME: 2.30 o'clock
LOCATION: College West 307.20 (Math & Stats Lounge)
TITLE: The scaling limit of loop-erased random walk in five dimensions and
above
ABSTRACT: The understanding of the connections between grid-based models
and continuous processes is a project of fundamental importance in modern prob-
ability research. One way to define a continuous process is by taking a scaling
limit of a discrete process. Brownian motion and loop-erased random walk are
two processes closely related. Brownian motion is among the simplest continuous
time stochastic processes, and as a continuous process, it can be defined by tak-
ing the scaling limit of a loop-erased random walk. A loop-erased random walk
is defined as a process obtained by taking a simple random walk and, whenever
the random walk hits its path, removing the resulting loop and continuing. The
scaling limit of loop-erased random walk in five dimensions and above is the eas-
iest case to analyze. In this case it turns out that there the intersections are only

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics