Anatomy of an extreme event: What can we infer about the history of a heavy-tailed random walk?

Extreme events are by nature rare and difficult to predict, yet are often much more important than frequent, typical events. An interesting counterpoint to the prediction of such events is their retrodiction-given a process in an outlier state, how did the events leading up to this endpoint unfold? In particular, was there only a single, massive event, or was the history a composite of multiple, smaller but still significant events? To investigate this problem we take heavy-tailed stochastic processes (specifically, the symmetric, α-stable Lévy processes) as prototypical random walks. A natural and useful characteristic scale arises from the analysis of processes conditioned to arrive in a particular final state (Lévy bridges).

#MaskOn! #MaskOff! Digital polarization of mask-wearing in the United States during COVID-19.

The coronavirus disease 2019 (COVID-19) has caused an unprecedented public health crisis worldwide. Its intense politicization constantly made headlines, especially regarding the use of face masks as a safety precaution. However, the extent to which public opinion is polarized on wearing masks has remained anecdotal and the verbal representation of this polarization has not been explored.