On Moebius duality and Coarse-Graining
| Autor: | Thierry Huillet, Servet Martínez |
|---|---|
| Přispěvatelé: | Laboratoire de Physique Théorique et Modélisation (LPTM - UMR 8089), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), Departamento de Ingenieria Matematica, Centro Modelamiento Matematico, Universidad de Santiago de Chile [Santiago] (USACH)-Centro Modelamiento Matematico (CMM), CONICYT BASAL-CMM project PFB |
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
coalescence 021103 operations research Duality Mathematics::Number Theory General Mathematics Probability (math.PR) 0211 other engineering and technologies coarse-graining 02 engineering and technology 01 natural sciences Moebius matrices Combinatorics [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 010104 statistics & probability Monotone polygon partitions FOS: Mathematics Sylvester formula Granularity 0101 mathematics Statistics Probability and Uncertainty Mathematics - Probability Mathematics |
| Zdroj: | Journal of Theoretical Probability Journal of Theoretical Probability, Springer, 2014, pp.online first. ⟨10.1007/s10959-014-0569-5⟩ |
| ISSN: | 0894-9840 1572-9230 |
| DOI: | 10.1007/s10959-014-0569-5⟩ |
| Popis: | We study duality relations for zeta and M\"{o}bius 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 M\"{o}bius 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 M\"{o}bius 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. Comment: accepted in Journal of Theoretical Probability |
| Databáze: | OpenAIRE |
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