The limit surface of antichains in the 3-dimensional random partial order

Stochastic Analysis Seminar Series

An antichain is a set of elements of a partially ordered set which are pairwise incomparable. In the co-ordinatewise partial order on R^k, two points x and y satisfy x < y if and only if x_i < y_i for each co-ordinate i.  The induced partial order on a set X_n of n independent and uniformly distributed points in [0,1]^k is called the random k-dimensional partial order. 

This model was introduced by Peter Winkler and subsequently studied by Bollobas, Brightwell and Sidorenko.We study the probability that the random k-dimensional partial order is an antichain, and the typical distribution of the set X_n conditional on being an antichain, in the limit as n tends to infinity.  It is about a joint project with Nic Georgiou, in which we have had useful input from Cedric Boutillier, Graham Brightwell, Rick Kenyon and Mark Walters.


Edward Crane (Bristol)

Monday, October 29, 2012 - 14:15
to 15:15