Is there any way of limiting the space devoted to log files?
Since we are talking about the result of application crashes, if such files keep on building up, I would pursue the reason of why this happens in the first place.  Once fixed, just dump the files manually and move on.

On a stable system, the folder ~/Library/Logs/CrashReporter should be empty.  Having almost 2 GB of crash dumps means that there is (or was) something wrong.

As you probably know, log files and crash dumps can be used to diagnose issues on your computer in order to repair said issues.  Blindly removing them, will get you some disk space back, but the original issue will still be there and you will not be happy on the long run.

Due to the reason mentioned above (second paragraph of this answer), there is no automated task to limit the space for those files.  You could, if you are into scripting or Automator (or both), write a script or Automator Folder Action workflow (or a combination of both) and watch that folder's size and when reaching a threshold removing the oldest entries.