Семинар по Анализу и Вероятности факультета математики ВШЭ. Доклад Scaling limit of a population model with age / Предел масштабирования популяционной модели с учетом возраста

Abstract. Consider the following simple dynamics. We start with a semi-infinite binary vector ((\ldots,X_{-1},X_0)). At each step, we draw a geometric random variable (Z), look (Z) steps into the past, and copy the bit we see at that position. This dynamics can be interpreted as a modification of the Moran model, in which the probability that an individual passes a trait (represented by a binary bit) to a given descendant is a function of its age and decays exponentially in time. When the parameter of the geometric random variable converges to 1, we show that the expected future value of the trait converges to a solution of the Wright–Fisher equation. For suitable generalizations of this model, we show that their scaling limits are given by solutions of the Fleming–Viot equation. Joint work with Eldon Barros and Eric Santana (IMPA).

We warmly invite you to attend the meeting of the seminar. Please feel free to share this announcement with colleagues and students who might be interested.

We look forward to your participation!

 Best regards,
Alexander Menovschikov
on behalf of the organizing committee

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