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Seattle, WA
New York,NY
Petaluma, CA
Jacksonville, FL
Houston, TX
Figure 15.3 Short time trajectories of dollar bills in the United States. Lines connect origin
and destination locations of bank notes that traveled for less than a week. Figure from
Brockmann et al.
(
2006
).
and it implies that bank note dispersal lacks a typical length scale resembling
Levy flights. Levy flights are superdiffusive; they disperse faster than ordinary
randomwalks. This discoverywas amajor breakthrough in understanding human
mobility on global scales. In light of this discovery, in dispersal humans are
similar to animals.
However, our intuition suggests that we do not move completely at random.
There are regularities in our lives: most of us have a home, a workplace, a
hobby. These activities necessarily shape our trajectories. Instead, if we do
follow a pure Levy flight we rarely find our way back home, but our position
increasingly moves away from the initial one.
To further investigate human mobility patterns, in 2008 Barabasi and his team
analyzed the trajectories of 100,000 anonymized mobile phone users whose
positions were tracked for a six-month period. Contrary to bills, mobile phones
are carried by the same individual during his or her daily routine, offering the
best proxy to capture individual human trajectories. An immediate result of the
research was that the distribution of displacements
r
between a user's positions
at consecutive calls is well approximated by a truncated power law:
P
(
r
)
=
(
r
+
r
0
)
−
β
exp
(
−
r/κ
)
with exponent
β
=
1
.
5 km, and some cutoff values
κ
.Such
equation suggests that human motion follows a truncated Levy flight, apparently
confirming in a certain way observations on bank notes. However, differences
1
.
75
±
0
.
15,
r
0
=
