A Note on Matrix Concentration Inequalities via the Method of   Exchangeable Pairs
  The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs". Along the way, we prove new trace inequalities for the matrix exponential. 
Daniel Paulin
math.PR math.FA