3/4 -- In a statement, Peter tells us, "I understand the seriousness of the allegations that have been filed against me, however the allegations are false. I do have faith in the judicial process and have no doubt that I will be acquitted from any wrong doing. While I can offer no further information about this incident, I do confirm that my attorney is handling this matter expeditiously."

'Real Housewives of Atlanta' star Peter Thomas just got arrested in Miami on an out of state warrant ... TMZ has learned.

Law enforcement sources tell TMZ ... Peter was busted Friday after getting off a plane at Miami International Airport. We're told he was taken into custody on a warrant from Louisiana for allegedly writing fake checks, and he's being held without bond.

You might remember Peter from the time he pulled a knife on Kenya Moore's ex, Matt Jordan, during a brawl in the middle of a radio interview. He claimed self-defense.

Peter and Cynthia Bailey got married on season 3 of 'RHOA' -- but they separated back in 2016. He still appears on the show every once in a while, usually with his stepdaughter, Noelle Robinson.

Story developing ...