CM-AMO Seminar | Power laws: pinning the tail on the shoulder

Speaker: Nadav Shnerb Bar (Ilan University, Ramat Gan, Israel)

The appearance of fat-tailed and scale-free distributions is frequently attributed to an
underlying multiplicative stochastic dynamics. The most salient process considered in this
context is the “rich get richer” mechanism (aka preferential attachment, Yule process etc.) that
involves birth and mutations. Any new agent either joins an existing group with a chance
proportional to its size (birth) or creates a new group (mutation). In most cases, however, some
“death” process already exists: animals die, leaving species goes extinct and internet
connections break down. A universal solution for the birth-death-mutation process will be
presented. The new solution allows for much better inference of the underlying process
parameters: in particular it allows extracting information from the “shoulder” of the distribution
at small values, instead of using only the power-law tail. Examples from various branches of
science – ecology, genetics, and social networks - will be discussed.