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سمينارهاي هفتگي خانه رياضيات: پروفسور حسام محمود:The class of tenable zero balanced polya urn schemes : characterization and gaussian phases

خانه رياضيات اصفهان

we study a class of tenable irreducible non degenerate zero-balanced polya urn schemes . we give a full characterization of the class by sufficient and necessary conditions.only forms with a certain cyclic structure in their replacement matrix are admissible. the scheme has a steady state into proportions governed by the principal eigenvector of the average replacement matrix:. we study the gradual change for any such urn containing n balls from the initial condition to the steady state . we look at the status of an urn starting with a positive proportion of each color after j draws . we identify three phases of j : the growing sub linear . the linear . and thesuper linear . in the growing sub linear phase the number of balls of different colors has an asymptotic joint multivariate normal distribution , with mena and covariance structure that are influenced by the initial conditions .

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