An embedding for the Kesten-Spitzer random walk in random scenery
  For one-dimensional simple random walk in a general i.i.d. scenery and its limiting process we construct a coupling with explicit rate of approximation extending a recent result for Gaussian sceneries due to Khoshnevisan and Lewis. Furthermore we explicity identify the constant in the law of iterated logarithm. 
Endre Cs\'aki, Wolfgang K\"onig (Fields Institute/Techniche   Universit\"at Berlin), Zhan Shi