There is no sign of Edgar Ramirez (Gianni Versace), Antonio D'Amico (Ricky Martin) or the brilliant Penelope Cruz (Donatella Versace), who has been one of the series' brightest sparks so far.

Thankfully, the writers succeed in endearing the new characters to us quite quickly, and Darren Criss continues to do his creepy best as the killer at the heart of the story.

As with previous episodes, the story is a mixture of fact, sources pulled from the book the series is based on - Vanity Fair journalist Maureen Orth's Vulgar Favours - and fiction crafted by the show's writers for dramatic effect.

Read on to find out about the background to the series by showrunner Ryan Murphy and writer Tom Rob Smith.

Or, check out our guides to fact and fiction in episode 1 and episode 2.

Episode 3: A Random Killing

Who were Lee and Marilyn Miglin?

The episode opens with Marilyn Miglin, a well-to-do middle aged woman flogging a pheromone perfume on a QVC-type shopping channel in Toronto, Canada. Then, it follows her as she flies back her hometown of Chicago, where her husband, Lee Miglin, is meant to be picking her up from the airport. He doesn't show up.

She arrives at the house and, finding a tub of melted ice cream out on the counter and no sign of Lee, alerts the police.

The police search the house, finding nothing – until they arrive in the garage to discover a body. As someone goes to tell Marilyn what happened, she says, "I knew it".

What we know to be true:

On the morning of 4th May 1997, the body of real estate developer Lee Miglin (aged 72) was discovered at his home in Chicago. His wife Marilyn, who according to journalist Orth was a "fixture of the home shopping network", was indeed returning from Canada when his body was discovered. The two had been married for 37 years.

Lee's status - he was a millionaire with ties to then-mayor Richard M Daley - appears to have had a significant impact on the status of the Cunanan case.

"Before that, I don’t even remember having any knowledge that there was a guy who killed two other men," Miami Herald editorial board member Luisa Yanez told Vulture, "but with Miglin, he was well known. This was somebody prominent in the community of Chicago. Things changed after Miglin. People are really looking for Cunanan now. This is not just a guy killing people he knows. Now he’s a spree killer.”

Did Lee know Andrew Cunanan?

The drama then reverts back in time to before Marilyn goes away for the weekend. After a couple of allusions to Lee's secret homosexuality, he receives a call from Andrew Cunanan, who says he'll be in Chicago soon. Lee makes an excuse as to why he won't be joining Marilyn, and invites Cunanan over.

It is suggested that the two have had a relationship - that Cunanan is an escort who Lee pays for sex and companionship.

What we know to be true:

"I can tell you unequivocally that we have not found a link between Andrew Cunanan and anyone in the Miglin family," Matt Rodriguez, former Chicago police superintendent, said in July 1997.

But there has been much speculation to the contrary. According to a New York Times report around the time of the murder based on testimonies of Cunanan's acquaintances in San Diego, he was friendly with Lee's son Duke.

The FBI file on Cunanan quotes an unnamed, Chicago-based "rent boy" who claims that Miglin and his killer had picked him up in a car and had sexual relations with him.

"That relationship would explain, for the first time with some certainty, how Cunanan knew the 72-year-old Miglin and had knowledge of where he lived on the Gold Coast," ABC7 Chicago reported upon the release of the FBI document, "and why he felt comfortable going into Miglin's home after the murder and making a sandwich for himself."

Miglin's son Duke said in 2017 that he did not believe there was any connection between Miglin and Cunanan.

The specifics of the murder

Much as in episode two, Andrew's sex games take a dark turn with Lee, but this time he kills his victim.

He wraps Lee's face in duct tape and binds his legs with an extension cord, before dropping a bag of concrete on him, and then stabs him several times with a screwdriver. He then dresses the body with women's panties and scatters gay porn magazines around the crime scene.

"Lee Miglin's murder was horrendously brutal - the most vicious of all Andrew Cunanan's crimes," Orth writes in Vulgar Favours. She reports that his body, which had been severely brutalised, was found next to gay porn magazines as portrayed in the series. “His ribs had been broken, and he had been tortured with four stabs in the chest, probably with garden shears," she says. "His throat had been cut open with a garden bow saw.”

However, Orth's book does not mention women's underwear: "Lee Miglin was wearing black Calvin Klein bikini underwear trimmed in white," she writes.

American Crime Story executive producer Brad Simpson told the Chicago Sun Times that the episode “dramatise[s] what we believe happened that weekend starting from the established facts of the crime scene. Based on the evidence, we believe that Lee and Andrew did know each other, and [that] Andrew’s attack, as with all his victims except for William Reese, was targeted and specific. We used Maureen Orth’s book and consultancy, as well as the FBI records and the statements from witnesses inside the records for research and background.”

The police slip up

Soon after Miglin's body is found in episode three, a truck, belonging to Cunanan's previous victim David Madsen, is found near the Miglins' home. At this point, Cunanan becomes the prime suspect in the murder, and the police soon realise that Miglin's Lexus – which the murderer had stolen – had a phone that could be tracked.

However, this information is leaked out to the press soon after the discovery is made. Cunanan hears a report on the radio which says as much. He tries to tear out the antennae, before ditching the car and stealing another, killing his fourth victim, cemetery worker William Reese, in the process.

What we know to be true:

On Thursday 8th May, just days after the murder, the FBI and Chicago police were informed that the telephone in Lee Miglin's Lexus had been activated in the Philadelphia area. Chicago authorities informed the Philadelphia police.

"The next morning," Orth writes, The Chicago Tribune ran a story - which reporter Andrew Martin says was based on a law enforcement leak in Chicago - saying that Andrew had used the cell phone and was being tracked."

Soon after, radio in Philadelphia broadcast that Miglin's car phone had been tracked.

"Clearly Andrew was listening," she says. "This unfortunate leak out of Chicago, followed by the police confirmation of it, was probably the most serious blunder of the entire manhunt. The consequences were later revealed in the inspection of the Lexus."

"The phone antenna was completely torn out, so he obviously heard it right away and tried to dismantle the cell phone,'" Chicago county sergeant Todd Rivard told her in the book.

It was the closest the authorities came to stopping Cunanan.

The Assassination of Gianni Versace airs Wednesday at 9pm on BBC2