MADISON, Wis. -- Two incidents this week at State Street's Peace Park have left one man in critical condition and two others in police custody connected to a pair of fights.

Peace Park is a gathering spot for panhandlers -- one of the few areas city ordinances allow them to be.

Nearby business owners and panhandlers said they're not concerned about the violence because it's not random.

On Monday night, a homeless strangled another homeless man in a fight allegedly over a woman.

"The thing that happened on Sunday is very unfortunate, but I really want to iterate though, it's not random," said Hawk Schenkel, a State Street business owner. "No one is just walking by and getting hurt, not a single person has ever walked by Peace Park and got randomly hurt."

"I'm really not worried this is probably the safest street in Madison," said Reggie McDaniel, a panhandler. "More people come down this street than any other."

Police said that they're not alarmed either.

"Is the person on the street gonna be accosted? No," said Madison Police Capt. Mary Schauf. "We don't have reason to believe that's true. State Street is still a place to come, and there's a lot of space for a lot of people."

Investigators said that they have successfully collected some evidence from a camera on State Street.

Renovations are scheduled to start in the park later this year, officials said.

Schenkel said an enhanced family friendly atmosphere, will better accommodate events, and will help dissipate the crowd, easing the tension, and slowing the number of incidents in the park.