Filed under: Deals, Private equity, Hilton Hotels (HLT), Blackstone Group L.P (BX)Is private equity really dead? Well, it looks like the death has been widely exaggerated. Not only has KKR filed to go public, but the newly public Blackstone Group LP (NYSE: BX) has agreed to buy Hilton Hotels Corp. (NYSE: HLT) for a cool $26 billion.It was back in 1919 that Conrad Hilton purchased his first hotel in Cisco, Texas. He certainly had lots of drive and ambition.Now, the company has 2,800 hotels and 480,000 rooms across 76 countries. But, the company thinks it's better keeping things private (at least for now). And, hey, why not take billions from the hungry Blackstone?The deal comes at $47.50 or a 40% premium from yesterday's closing stock price. When the ...