So here's the deal. Since the Z10 has been released, I have used several different Z10 units (probably 7 or 8... I lost count) across four different carriers, and I have never once experienced a random reboot on my Z10. The same goes for all of the members of the CrackBerry editorial team - there have been very few mentions of the phone randomly rebooting for no reason.
However, if you jump into CrackBerry's crazy busy BlackBerry Z10 forums, you will find a LOT of discussion around owners experiencing their Z10 randomly restarting, either during the day, or during the night while it's on the charger. For some, it seems to be a once per week thing. For others, it's happening daily. It felt like the reboot issue has most-often been reported by users on Verizon - to be certain, the reports in the forums do seem disproportionately high for Verizon Z10 owners compared to other carriers, but as you dive through the forum threads it is an issue that is definitely reported by at least some users across carriers around the globe.
Have you experienced randoom reboots on your BlackBerry Z10?