Simulations of Two-dimensional Simple Random Walk and Loop-Erased Random Walk

Last modified: July 9, 2007

Here is an applet for simulating two-dimensional simple random walk (SRW) and loop-erased random walk (LERW). This is a work in progress, but seems to perform reasonably well. It will continue to be updated as improvements are made.

The parameter Num steps gives the number of steps in the random walk. Choose something large, say 10000. Changing the random seed will produce different realizations.

Select the type (SRW) or (LERW) of process you would like to simulate. Notice the similarities between the simulations of LERW and the simulations of SLE₂.

This applet was written by Kevin Petrychyn of the University of Regina.