Doctor Vsevolod Shneer, Heriot-Watt University, Edinburgh
We will consider a range of models motivated by various protocols for transmitting messages in wireless communication networks. Among these protocols and the well-known MaxWeight, alpha-fair, CSMA and others. We will consider questions of stability and throughput achieved by networks governed by these protocols.
Doctor Fraser Daly, Heriot-Watt University, Edinburgh
The Stein-Chen method is a powerful modern technique for obtaining explicit error bounds in probability approximation, even in the presence of relatively intricate dependence between the underlying random variables. This method has its origins in the pioneering work of Charles Stein and Louis Chen in the 1960s and 70s on Gaussian and Poisson approximations, respectively, for sums of dependent random variables. Since then, the same techniques have been applied to a variety of univariate, multivariate and process-level approximations. In this course we will begin with an overview of the Stein-Chen method, focusing firstly on the classical Gaussian and Poisson cases. We will illustrate the technique with classical limit theorems and approximations for sums of locally dependent random variables. Our focus for the majority of the course will be on how coupling constructions can be applied in conjunction with the Stein-Chen method to yield explicit approximations in a variety of settings. This will include generalizations and extensions of Poisson approximation results (for example, to compound Poisson approximation), and approximation by geometric sums, with Markov chain passage times our main application here. Other examples and applications will be visited and revisited throughout the course, including approximations for runs in Bernoulli trials and for extreme values. We will also see how some of the techniques we consider may be extended to approximations on the level of stochastic processes.
Professor Sergey Foss, Heriot-Watt University, Edinburgh and Novosibirsk State University, Novosibirsk
The short course includes three lectures:
"Spring School in Advanced Probability" is supported by Mathematical Center
in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of
Science and Higher Education of the Russian Federation.
will take place at Novosibirsk State University and
will consist of two 10-hour lecture courses taught in english.
In addition to the courses, there will be several workshops to discuss
the lectures and a poster session for students.
We are happy to see participants from any university and
invite them to prepare and present their own poster
The Mathematical Center in Academgorodok may provide
financial assistance towards travel and accommodation costs.
After our School, from the 10th to 13th of April,
Novosibirsk State University hosts the traditional
International Scientific Student Conference (ISSK-2020).
We invite you to take part in the section "Probability theory".
You can apply for participation until February 21th.
For more details please visit the conference