Under this theory the word was influenced by Old French vagant, vagaunt "wandering," from Latin vagantem (nominative vagans), past participle of vagari "to wander, stroll about" (see vagary). But on another theory the Anglo-French word ultimately is from Old French vagant, with an unetymological -r-. Middle English also had vagaunt "wandering, without fixed abode" (late 14c.), from Old French vagant.
1690s, "aggressive, boisterous," a Scottish word of uncertain origin, probably from rand "to rave," an obsolete variant of rant (v.). "In early use always of beggars, and probably implying vagrant habits as well as rude behavior. Now applied only to women" [OED]. The sense of "lewd, lustful, noisily wanton" is attested by 1847. Compare Scottish and northern English randy (n.) "a sturdy beggar or vagrant" (of males); "a noisy hoyden, a rude, romping girl." Related: Randiness.
1872, "miserly person," formerly "poor white migrant to California" (1860), earlier Pike (1854), perhaps originally "vagrant who wanders the pike (n.4)" (which is the notion in Sussex dialectal piker "vagrant, tramp, gypsy," 1838), but Barnhart, OED and others suggest the American English word ultimately is a reference to people from Pike County, Missouri. Its appearance seems too late to connect it with Middle English piker "robber, petty thief" (c. 1300, attested as late as 1549 in OED), from the source of pick (v.) in its sense of "steal, rob, plunder" (early 14c.) with its former long vowel.