My Erdös number is 4 via the following path:

Valerio Cappellini coauthored with Karol Życzkowski − MR2295806
Karol Życzkowski coauthored with Ofer Zeitouni − MR3039370
Ofer Zeitouni coauthored with Persi W. Diaconis − MR2044670 (2005e:60232)
Persi W. Diaconis coauthored with Paul Erdös − MR2126886 (2005m:60011)