Overhead of table with empty partitions

Say I've got a table that's partitioned by day and has 30 days worth of partitions. Every 30 days I'll create another 30 days worth of partitions and drop the previous 30 days worth. Stats are running everyday so the thinking is that having 29 or so days worth of empty partitoins will not cause any SQL performance issues. Testing has shown this to be the case, but wanted to see if there's any insight on having many empty partitions.

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