|Location:||MSRI: Baker Board Room|
random variables. One of the main pedagogical difficulties in this subject is that of motivating the definition of
free independence, which at first blush appears to come out of thin air. I will review the notion of classical independence and illustrate its relationship with the enumeration of connected graphs, and then attempt to "rediscover" the definition of free independence by considering a non-standard graphical enumeration problem. My hope is that this approach will be accessible to a general audience; in particular, no knowledge of operator algebras is required. One advantage of this approach, beyond its elementary character, is that the particular significance of the semicircle law in free probability will be clear from the outset. If time permits, I will outline Speicher's proof of the fact that classical independence and free independence are the only universal product constructions.