IMA Complex Systems Seminar

1:30, Thursday, April 8, 2004              



Incomplete U-statistics, random permanents and beyond


Greg Rempala

Department of Mathematics
University of Louisville
Louisville, KY  40292  USA



The talk will present some recent results from the general theory of the incomplete U-statistics of increasing order. In particular, the concepts of the so-called "permanent " and "minimal" designs will be developed.  These designs turn out to be asymptotically efficient as well as (under some conditions on the kernel functions) optimal with respect to the minimal variance criterion.   Applications of this theory to investigating asymptotic behavior of a random permanent function (for instance for counting matchings in a bipartite random graph), general sub-sampling methods, as well as and some problems in the protein sequences alignments will be discussed.