Free entropy and property T factors

We show that a large class of finite factors has free entropy dimension less than or equal to one. This class includes all prime factors and many property T factors.

The repetition of large-earthquake ruptures.

This survey of well-documented repeated fault rupture confirms that some faults have exhibited a "characteristic" behavior during repeated large earthquakes--that is, the magnitude, distribution, and style of slip on the fault has repeated during two or more consecutive events. In two cases faults exhibit slip functions that vary little from earthquake to earthquake. In one other well-documented case, however, fault lengths contrast markedly for two consecutive ruptures, but the amount of offset at individual sites was similar. Adjacent individual patches, 10 km or more in length, failed singly during one event and in tandem during the other. More complex cases of repetition may also represent the failure of several distinct patches. The faults of the 1992 Landers earthquake provide an instructive example of such complexity. Together, these examples suggest that large earthquakes commonly result from the failure of one or more patches, each characterized by a slip function that is roughly invariant through consecutive earthquake cycles. The persistence of these slip-patches through two or more large earthquakes indicates that some quasi-invariant physical property controls the pattern and magnitude of slip. These data seem incompatible with theoretical models that produce slip distributions that are highly variable in consecutive large events.