Consider the above diagram.
Here the sender initially wants to send 10000 B in a segment to the receiver but the window / buffer capacity of receiver is 0 i.e. full. Thus, the receiver cannot accommodate any bytes in its window. So, in reply the receiver sends the acknowledgement to the sender indicating its advertising window size is 0 and the sender should not send any other bytes to it until the window / buffer on the receiver side is not full.
After a period of time the sender sends 1 byte ( dummy byte ) to the receiver to know whether the receiver has some space in its window or not. This period of time is known as persistent timer. Now suppose the receiver window is still full and so in reply it again sends the acknowledgement to the sender that it cant accommodate any other bytes. And again if this process goes on and on, then actually no useful work is being done by the sender. This phenomenon is called silly window syndrome.
This is how both the two are related.