Hi- I did not spec the appliances for this job, so I don't know if the microwave is just re-circulating or actually venting. Since the sink wall is exterior- it's likely it's vented.

To determine if your over the range microwave is vented outside, please take a look inside the cabinet above to see if there is a vent. Also,it could be rear vented, where you would see a vent behind the microwave outside the house. This looks like Ge model# JVM1850 (vented model) or JNM1851 (non-vented model). The model number is located inside this microwave, and is another way to tell if it's vented model or not.