title: Probabilities for large events in driven threshold systems.
abstract: Many driven threshold systems display a spectrum of avalanche event sizes, often characterized by power-law scaling. An important problem is to compute probabilities of the largest events ("Black Swans"). We develop a data-driven approach to the problem by transforming to the event index frame, and relating this to Shannon information. For earthquakes, we find the 12-month probability for magnitude m>6 earthquakes in California increases from about 30% after the last event, to 40%-50% prior to the next one.
authors.affiliation: Department of Physics, University of California, Davis, California 95616, USA.
authors.forename: John B
authors.initials: JB
authors.lastname: Rundle
authors.forename: James R
authors.initials: JR
authors.lastname: Holliday
authors.forename: William R
authors.initials: WR
authors.lastname: Graves
authors.forename: Donald L
authors.initials: DL
authors.lastname: Turcotte
authors.forename: Kristy F
authors.initials: KF
authors.lastname: Tiampo
authors.forename: William
authors.initials: W
authors.lastname: Klein