Interesting question, Michael. From the far-field triggering point of view this might
be expected. When a large quake occurs earthquakes might be triggered by seismic
effects earlier than they would otherwise have happened. This would suggest that
since they are no longer happening when they otherwise would have, then that
period should see a lull in overall activity.
The Peru earthquake occurred on June 23, 2001. Checking the timing of previous
quiet periods vs. preceding large or great earthquake in the past few years should
tell if this is a reasonable time lag for effects.

8.3 days 3/18/94 to 3/26/1994 Mar. 9, 1994 Mw 7.6 Tonga Isl. 9 days to quiet
8.3 days 12/19/94 to 12/27/1994 Nov. 14, 1994 Mw 7.1 Philippines 1 mo. 5 days to quiet
11.0 days 12/10/96 to 12/21/1996 Nov. 11, 1996 Mw 7.8 Peru 1 mo to quiet
8.4 days 12/22/97 to 12/30/1997 Dec 5, 1997 Mw 7.7 Kermadec Is. 17 days to quiet
7.4 days 4/03/98 to 4/10/1998 Mar. 25, 1998 Mw 8.8 Macquarie Is. 9 days to quiet
12.7 days 4/12/98 to 4/25/1998 Mar 25, 1998 Mw 8.8 Macquarie Is. 18 days to quiet
and
8 days 8/13/2001 to 8/21/2001 Jun 23, 2001 Mw 8.2 Peru 1 mo 20 days to quiet

It appears that there might be something to this. The longest quiet periods
occur within about a month after the largest earthquakes in recent history.
There appear to be two possibilities - 1) after the initial 8-10 days of seismic
activation, a quiet period ensues and 2) about a month after the seismic
period occurs. My guess is that this quiet period probably was related to the
earthquake in Peru as a lull after the activation of far-field aftershocks. It would
require a lot more research, however to be sure.