  We study the shrinking Pearson random walk in two dimensions and greater, in
which the direction of the Nth is random and its length equals lambda^{N-1},
with lambda<1. As lambda increases past a critical value lambda_c, the endpoint
distribution in two dimensions, P(r), changes from having a global maximum away
from the origin to being peaked at the origin. The probability distribution for
a single coordinate, P(x), undergoes a similar transition, but exhibits
multiple maxima on a fine length scale for lambda close to lambda_c. We
numerically determine P(r) and P(x) by applying a known algorithm that
accurately inverts the exact Bessel function product form of the Fourier
transform for the probability distributions.

Data Analysis, Statistics and Probability;Statistical Mechanics