how do the major stable coins maintain their price? 

more specific the answer the better

Building @warpcast and @farcaster / dad / like to read, cook, ski, code

arbitrage? 
if usdc falls to .99 then someone can buy it on open market then redeem with circle and get 1.00, the buy tx increases the price on the open market. 
if it goes to 1.01 then someone can issue new usdc with circle and sell it on the open market for profit moving the price down.

yeah not sure about details. i'm assuming circle has a permissioned list of entities that can issue/redeem. everyone who can is strongly incentivized to do the arb. and yeah circle is probably doing the majority of that.

high level ok but interested in more details

how do you redeem or issue? specific contracts or forms
who is actually doing this arbing? I'd assume Circle would be incentivized to do this themself