Columnstore indexes are built and processed completely in memory. You will receive an out-of-memory error if you do not have enough memory to build the columnstore index. Column store processing is optimized for in-memory processing, however, they do not reside in memory after they are created. The index data is initially stored on disk. It is loaded into memory just like a row index is, and will then have the benefit of being in cache. Only the columns needed must be read. Therefore, less data is read from disk to memory and later moved from memory to processor cache, thereby providing a big performance benefit. The whole index is not stored in memory like PowerPivot. A columnstore index is persisted on disk just like any other index.
More info:
SQL Server Columnstore Index FAQ
Video Overview of the columnstore feature
