Perierchomai (G4022) combines peri (around) and erchomai (to go/come) to mean 'to go around,' 'to wander,' or 'to travel about.' Used of the seven sons of Sceva who wandered as exorcists (Acts 19:13), of disreputable widows who gad about (1 Tim 5:13), and of those who wandered in sheepskins (Heb 11:37-38).
The three uses of perierchomai in the NT form a remarkable contrast. Acts 19:13 describes the sons of Sceva wandering as exorcists without divine authority — and being overcome by the very demon they tried to cast out. 1 Timothy 5:13 warns of idleness leading to gadding about and saying what they should not. But Hebrews 11:38 transforms the word: those who wandered in deserts, mountains, caves, and holes in the ground — 'of whom the world was not worthy' — were not vagrants but heroes of faith. The same word, perierchomai, covers both purposeless wandering and Spirit-directed pilgrimage. The difference is not the path but the One who called you to it.