Record-dependent measures on the symmetric groups

A probability measure P[subscript n] on the symmetric group S[subscript n] is said to be record-dependent if P[subscript n]( σ ) depends only on the set of records of a permutation σ ∈ S[subscript n]. A sequence P = ( P n )[subscript n ∈ N] of consistent record-dependent measures determines a random order on N. In this paper we describe the extreme elements of the convex set of such P. This problem turns out to be related to the study of asymptotic behavior of permutation-valued growth processes, to random extensions of partial orders, and to the measures on the Young-Fibonacci lattice

Probability, Trees and Algorithms

The subject of this workshop were probabilistic aspects of algorithms for fundamental problems such as sorting, searching, selecting of and within data, random permutations, algorithms based on combinatorial trees or search trees, continuous limits of random trees and random graphs as well as random geometric graphs. The deeper understanding of the complexity of such algorithms and of shape characteristics of large discrete structures require probabilistic models and an asymptotic analysis of random discrete structures. The talks of this workshop focused on probabilistic, combinatorial and analytic techniques to study asymptotic properties of large random combinatorial structures