String Thermalization at a Black Hole Horizon
  Susskind has recently shown that a relativistic string approaching the event horizon of a black hole spreads in both the transverse and longitudinal directions in the reference frame of an outside observer. The transverse spreading can be described as a branching diffusion of wee string bits. This stochastic process provides a mechanism for thermalizing the quantum state of the string as it spreads across the stretched horizon. 
A. Mezhlumian, A. Peet and L. Thorlacius