On Moebius duality and Coarse-Graining
Year: 2014
Type: preprint
Abstract: We study duality relations for zeta and Möbius matrices and monotone conditions on the kernels. We focus on the cases of family of sets and partitions. The conditions for positivity of the dual kernels are stated in terms of the positive Möbius cone of functions, which is described in terms of Sylvester formulae. We study duality under coarse-graining and show that an $h-$transform is needed to preserve stochasticity. We give conditions in order that zeta and Möbius matrices admit coarse-graining, and we prove they are satisfied for sets and partitions. This is a source of relevant examples in genetics on the haploid and multi-allelic Cannings models.
Source: arXiv (Cornell University)
Authors: Huillet, Thierry, Martinez, Servet
Institution: Laboratoire de Physique Théorique et Modélisation
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951369599