Demography when history matters: construction and analysis of second-order matrix population models

Bernoulli matrix approach for matrix differential models of first-order

The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...

Second Order Asymptotics for Matrix Models

We study several-matrix models and show that when the potential is convex and a small perturbation of the Gaussian potential, the first order correction to the free energy can be expressed as a generating function for the enumeration of maps of genus one. In order to do that, we prove a central limit theorem for traces of words of the weakly interacting random matrices defined by these matrix m...

When Order Matters for Iterated Strict Dominance

We demonstrate that iterated elimination of strictly dominated strategies is an order dependent procedure. We also prove that order does not matter if strategy spaces are compact and payoff functions continuous. Examples show that this result is tight.

Review: Matrix Theory in Population Modelling Reviewed Work(s): A Consideration of Matrix Population Models: Construction, Analysis

bernoulli matrix approach for matrix differential models of first-order

the current paper contributes a novel framework for solving a class of linear matrix differential equations. to do so, the operational matrix of the derivative based on the shifted bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. an error estimation of presented method is provided. numerical experiments are...