ℐ–invariant random strict total orderings on ℤ
ULRICH MARTIN HIRTH · PAMM · 2003
Abstract In a recent preprint ([4]) Saul Jacka and Jon Warren develop further the ideas of Paul Ressel and myself [3], though they work without positive definite functions on semigroups. I approach the results of [4] on ℐ–invariant random strictly total orderings by semigroup methods as in [3]. These orderings are most directly related to card shuffling, cf. the rich work of Persi Diaconis. Although more concrete applications are not yet known to me, the related papers [3], [2] and [1] definitively do have a background in population genetics, so the present work on ℐ–invariant random orderings is certainly not far from real–life applications.