Harry Crane, Rutgers Experimental Mathematics Seminar, November 20, 2014
See part 1 at vimeo.com/112444717
Abstract: Historically, enumerative combinatorics and discrete probability theory are closely related through uniform probability distributions on finite sets. I will first explain why the uniform distribution is unnatural in some modern applications and then survey several aspects of non-uniform random partitions and permutations. The discussion touches on ideas from enumerative combinatorics, algebra, probability, and statistics. I assume no prior knowledge.