- RMITOpt Seminar – Dr. Robin Hill, Department of Electrical Engineering at the University of Melbourne
- RMITOpt Talk – Bui Thi Hoa (Federation University)
|Speaker: Prof. Peter Taylor,
School of Mathematics and Statistics, University of Melbourne: (Joint work with Dario Bini, Jeff Hunter, Guy Latouche, Beatrice Meini)
Title: Why is Kemeny’s constant a constant?
Date and Time: Friday, September 21st, 3.00pm – 4.00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus (To connect via visimeet please contact firstname.lastname@example.org)
|Abstract: In their 1960 book on finite Markov chains, Kemeny and Snell established that a certain sum is invariant. The value of this sum has become known as Kemeny’s constant. Various proofs for the invariance have been given over time, some more technical than others. We shall first give a simple algebraic proof and then follow it up with a probabilistic proof that gives physical insight into what is going on. The result extends without a hitch to continuous-time Markov chains on a finite state space.
For Markov chains with denumerably infinite state space, the constant may be infinite and even if it is finite, there is no guarantee that the physical argument will hold. We shall show that the physical interpretation does go through for the special case of a birth-and-death process with a finite value of Kemeny’s constant.
Bio: Peter Taylor received a BSc (Hons) and a PhD in Applied Mathematics from the University of Adelaide in 1980 and 1987 respectively. In between, he spent time working for the Australian Public Service in Canberra. After periods at the Universities of Western Australia and Adelaide, he moved at the beginning of 2002 to the University of Melbourne. In January 2003, he took up a position as the inaugural Professor of Operations Research. He was Head of the Department of Mathematics and Statistics from 2005 until 2010. Peter’s research interests lie in the fields of stochastic modelling and applied probability, with particular emphasis on applications in telecommunications, biological modelling, economics, healthcare and disaster management. He is regularly invited to present plenary papers at international conferences.
From 2002 to 2018, Peter was the Editor-in-Chief of Stochastic Models. He serves on the editorial board of Queueing Systems and, from the beginning of 2019, he will become the Editor-in-Chief of The Journal of Applied Probability and Advances in Applied Probability. He served on the Awards Committee of the Applied Probability Section of the Institute for Operations Research and Management Science (INFORMS) from 2005-2007 and has been co-chair of the INFORMS committee for the Nicholson Prize, awarded for the best student paper in operations research.
From February 2006 to February 2008, Peter was Chair of the Australia and New Zealand Division of Industrial and Applied Mathematics (ANZIAM), and from September 2010 to September 2012 he was the President of the Australian Mathematical Society. In 2013 he was awarded a Laureate Fellowship by the Australian Research Council and he is currently Director of the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS).