Dear GMS,
I hope you are all doing well.
We will have a seminar on 26th of January, Monday in 123 St. Paul's between 11:30 and 12:30. Our speaker is @Homer De Veramailto:deverahf@myumanitoba.ca. This is going to be the first talk of this semester. Lunch will be served as usual.
The details about his talk are below.
Title: Minimizing Kemeny's constant for partial stochastic matrices with a single specified column
Abstract: Given a finite, discrete-time, time-homogeneous Markov chain on n states with an irreducible transition matrix T, we may compute Kemeny's constant K(T) in terms of the eigenvalues of T. Kemeny's constant on such matrices may be interpreted in terms of the expected number of steps to get from a random initial state to a random destination state, and hence, may be viewed as average travel time on a network when the states of the Markov chain are viewed as vertices on a graph. We similarly define K(T) in terms of eigenvalues of a stochastic matrix T having a single essential class, an extension of irreducible stochastic matrices. Suppose we have a partial stochastic matrix where some entries are specified and the rest are unspecified, how do we choose values for the unspecified entries so that the resulting stochastic matrix has a single essential class and K(T) is minimized? Steve Kirkland solved this question for partial stochastic matrices where the only specified entries are the diagonal entries and where the only specified entries are in a single row. In this talk, we present our results for the case where the only specified entries are in a single column. This is a work in progress with Prof. Kirkland.
We have slots available for interested speakers! Please fill out this formhttps://forms.gle/gMgGoqTcBnadxhwu9 if you are interested.
See you all in the seminar! GMS Websitehttps://sites.google.com/view/umgradmathsociety/ / Instagramhttps://www.instagram.com/umgradmathsociety/
Sincerely, Berkanthttps://cnnk.xyz GMS Executive