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Random sieves and generalized leader-election procedures
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报告题目:Random sieves and generalized leader-election procedures
报告人:Alexander Marynych, 副教授,基辅大学
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邀请人:董从造
报告时间:2018年12月25日(周二)下午3:40-4:20
报告地点:信远楼II206数统院报告厅
报告人简介:Alexander Marynych received BSc and MSc degrees in applied mathematics from Taras Shevchenko National University of Kyiv (KNU) in 2007 and 2008, respectively. He got PhD from Utrecht University in 2011. In 2012, Dr. Marynych did a postdoc at Technical University of Eindhoven (Netherlands). He was Assistant Professor at the Faculty of Computer Science and Cybernetics at KNU in 2013-2014. Since 2017 he is an Associate Professor at KNU where he also defended his habilitation in 2017.
Dr. Marynych was engaged in a joint research project between KNU and Utrecht University (Netherlands) from 2009 to 2011. In 2015 he received a Humboldt Fellowship (德国洪堡基金) and spent two years as a research fellow in the University of Muenster (Germany). In 2018 he was a guest professor in University of Innsbruck (Austria).
Dr. Marynych authored one monograph besides 3 lecture notes and has published over 40 research papers in a variety of probability journals such as Annals of Probability, Annals of Applied Probability, Bernoulli, Stochastic Processes and Their Applications, Electronic Communications in Probability, Electronic Journal of Probability, etc.
The current research interests of Dr. Marynych are
(1) Renewal Theory, Shot Noise Processes, Random Processes with Immigration, Regenerative Compositions;
(2) Exchangeable Coalescents, Analysis of Random Recurrences; and
(3) Probabilistic Number Theory, Random Trees, Optimal Stopping.

报告摘要:Let R be an arbitrary infinite random subset of the set N of positive integers and R_k, k=1,2,… be independent copies of R. A random sieving of the set N by the set R is an infinite chain of countable sets S_k, k=0,1,2,… such that S_0=N and the set S_k is obtained from the set S_{k-1} by removing the elements of S_{k-1} with the indices outside of R_k. Some natural choices of the set R are:
(i) the range of an increasing integer-valued random walk;
(ii) the set of record’s positions in an infinite sample from a continuous distribution.
In the talk, which is based on two recent joint papers with G. Alsmeyer and Z. Kabluchko, I will discuss asymptotic properties of random sieves (i) and (ii), as well as their connections with the classical leader-election procedures, exchangeable coalescents and iterated random functions.

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