Database Reference
In-Depth Information
Figure 15.2 Brownian motion (darker curve on the right) is described as a random walk
in which all the steps give the same contribution. A Levy flight occurs when the trip is
dominated by a few very large steps.
15.1.2 Human Mobility Patterns
Are human movements similar to those of grains of pollen, following a Brownian
motion, or are they governed by Levy flight, like themovementsmarine predators
and monkeys? Or do they follow their own laws? To answer above questions,
we need to observe humans under a microscope, like Perrin observed atoms
and was able to experimentally confirm Einstein's theory. The technological
era, at last, allows us to track human mobility and to test models, thanks to the
exploding prevalence of mobile phones, GPS, and other handheld devices. Such
devices are our social microscopes. In 2006, Dirk Brockmann and his colleagues
proposed using the geographic circulation of bank notes in the United States
as proxy for human traffic, based on the idea that individuals transport money
as they travel. They analyzed data collected at the largest online bill-tracking
Web site,
www.wheresgeorge.com
, and found that most bills remain in the
vicinity of their initial entry, yet a small but a significant number have traversed
distances of the order of the size of the United States (Figure
15.3
), consistent
with the intuitive notion that short trips occur more frequently that long ones.
Brockmann's team calculated that the probability
P
(
r
) of a bank note traversing
a distance
r
follows a power law:
P
(
r
)
∼
r
−
(1
+
β
)
with an exponent
β
≈
0
.
6. Moreover, they found that the typical distance
X
(
t
)
from the initial starting point as a function of time is a power law:
X
(
t
)
∝
t
1
/β
.
As we know, for Brownian motion the distance
X
(
t
) scales according to the
square-root law. For a power law the variance diverge for exponents
β<
2
