Weak Limit of the 3-State Quantum Walk on the Line
  We revisit the one dimensional discrete time quantum walk with 3 states and the Grover coin. We derive analytic expressions for observed the localization, an long time approximation for the probability density function (PDF). We also connect the time averaged approximation to the PDF found by Inui et. al. to a spatial average of the walk. We show that this smooth approximation constitutes a proper PDF that predicts moments of the real PDF accurately. 
Stefan Falkner and Stefan Boettcher (Emory University)
quant-ph cond-mat.dis-nn