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After the recent update:
Google Android 4.3 (Jelly Bean)
14.2.A.1.136
2014-01-30
...my XPERIA Z1 turns the volume up and down automatically on notifications and ringtones, with the equipment on the table, without any touch, sometimes it rings with normal volume and other times it rings on low volume.
Have you tried clearing data for smart connect in settings-apps-all.