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Seminar on Probability and Statistics
Seminar information archive ～10/07｜Next seminar｜Future seminars 10/08～
| Organizer(s) | Nakahiro Yoshida, Hiroki Masuda, Teppei Ogihara, Yuta Koike |
|---|
2026/10/16
15:00-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Krzysztof Bartoszek (Department of Computer and Information Science, Linköping University)
An introduction to quadratic stochastic operators (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/JjtHEBHOT6m4SvmAcXrtWQ
Krzysztof Bartoszek (Department of Computer and Information Science, Linköping University)
An introduction to quadratic stochastic operators (English)
[ Abstract ]
Markov chains are inherently linear processes and also are not elegant for describing interactions between agents. For this end, non-linear models are needed, and quadratic stochastic operators (QSOs) are a first step. They describe mixing of two populations, e.g., sexual reproduction, where one parent comes from the female class and the other from the male class. Studying the law, even in the limit, of a population evolving under a QSO is a challenging task due to the interaction component between the two classes of individuals. Restricting the class of QSOs, to the so-called centred quadratic stochastic operators, one is able to show that, in the case of hermaphroditic species, when the offspring's trait is equal to an additively perturbed arithmetic mean of the parents' traits, one can represent the law of the trait in descendant populations through an appropriate sum of independent random variables. QSOs can be further generalized to an arbitrary number of parents, and cubic stochastic operators are the next step.
[ Reference URL ]Markov chains are inherently linear processes and also are not elegant for describing interactions between agents. For this end, non-linear models are needed, and quadratic stochastic operators (QSOs) are a first step. They describe mixing of two populations, e.g., sexual reproduction, where one parent comes from the female class and the other from the male class. Studying the law, even in the limit, of a population evolving under a QSO is a challenging task due to the interaction component between the two classes of individuals. Restricting the class of QSOs, to the so-called centred quadratic stochastic operators, one is able to show that, in the case of hermaphroditic species, when the offspring's trait is equal to an additively perturbed arithmetic mean of the parents' traits, one can represent the law of the trait in descendant populations through an appropriate sum of independent random variables. QSOs can be further generalized to an arbitrary number of parents, and cubic stochastic operators are the next step.
https://u-tokyo-ac-jp.zoom.us/meeting/register/JjtHEBHOT6m4SvmAcXrtWQ
