Are the magnitudes of earthquakes in Southern California, with incompleteness removed, correlated?

Summary The correlation between the magnitudes of earthquakes is a scientific question usually investigated by statistical seismologists. In the last decades, two opposite answers have been given to the problem of correlation of magnitudes: there is no correlation, i.e. the magnitude of earthquakes in a seismic catalog can be considered as random sampling from the magnitude distribution; or, there is a correlation, i.e. the magnitude of a seismic event can influence the magnitude of the successive event. Here we used the Southern California seismic catalog, properly treated to remove incompleteness, to answer the question, finding no significant correlation between magnitudes.