Multivariate Bernstein duality for tournament Wright--Fisher diffusions
Year: 2026
Type: preprint
Abstract: We give a probabilistic proof of a multivariate Bernstein duality for a multivariate Wright--Fisher frequency process with selection encoded by a finite tournament. The construction includes nontransitive interactions, such as rock--paper--scissors selection. Its dual is a pure-jump process of coefficient functions in the multinomial Bernstein basis. Selection increases the Bernstein degree through a winner--loser averaging operator, whereas neutral resampling decreases it through a duplication operator. For the proof, we construct a continuous forward process independently of duality, use duality to establish uniqueness, and obtain a weak stochastic differential equation representation and invariance of the simplex faces. This provides a sampling-based treatment of the tournament specialization of multitype Bernstein duality, extending an open problem in the binary Kingman setting of Cordero, Hummel, and Schertzer (2022).
Source: arXiv (Cornell University)
Author: Hernández, Osvaldo Angtuncio
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225835226
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